My logic puzzles

Second puzzle of my first blog. The reason the grid is not square was because when I wrote this puzzle (on paper), I miscounted the size of the grid, and then I didn't bother changing it. In my defense, I was still very new to puzzle-writing; I would have reworked it today.

I went back to the all-1 theme (or, as my past self called it, "Tents Akari"). When I posted this puzzle on my first blog, it was not unique and there's no sign I got any comment that said so. But when I ported it to my second blog, I made a stealth change to the puzzle that made it unique. This is said second version.

I don't remember what prompted me to write this puzzle, but I do know there are Akari puzzles with sophisticated (and often cursed) global deductions serving as the break-in. This is my attempt at writing one. I still like it.

Adding a variant to an existing genre, but I think this might have simply been taken from Palmer's Akari EX. Some reasonable aesthetic, but at the expense of pretty boring logic that doesn't explore the genre enough.

Speaking as a seasoned puzzle author nowadays, among the first 12 puzzles I've written (i.e. everything in my first blog before I abandoned it and moved to a different blog), I think this is my favorite. (If you're wondering, [2011-03-18] Slitherlink is likely my second.)

Named "Allure" as part of the Lust sin, and the fish were hearts instead, because you're reeling in love or something like that. Definitely a very stretched theme.

The puzzle itself is... fair. Nothing remarkable, I'd say, but that's not necessarily a bad thing for a contest.

Putting "99"s in Araf is always fun. For a small enough grid, it effectively means "infinity"; it's going to be the upper bound and it's going to be satisfied, you just need the lower bound. (I haven't seen an Araf puzzle that's big enough so that the "99" actually matters, e.g. the region ends up being size 98.) But using "99" means you don't need to describe what this "∞" symbol is in the rules. Of course, the other way around also works; you can use a negative number as the lower bound, but "1" also works and it's not as funny to see.

A basic deduction in Araf is that a region cannot have two numbers that are consecutive (differ by 1). That drove practically the entire theme.

After deciding I would start with rings, I put in consecutive numbers all around the ring, to force each clue to extend out and pair up elsewhere. I wanted to allow clues across in a single ring to pair up — just it couldn't be adjacent clues — so I put in the half-increasing, half-decreasing pattern. This way, clues across the grid are generally not consecutive. Once that basic theme is set up, I simply tweaked the starting (lowest) number and the offset of the rings, leading to these two rings of clues.

The rest of the puzzle likely came from realizing several of the clues couldn't pair up, so I had to put in additional clues. Since the rings had low-value clues, some of the unpaired clues were simply looking for another clue to pair up with, their sizes were already good. So I got cute and put in "99" clues, and apparently I managed to fit in four.

This puzzle is a toughie, but I really like the logic.

Mathematical puzzles are strange. Equations can be surprisingly restrictive. Sometimes the way forward with a puzzle involves brute force, listing down the possibilities of some equation to notice something. It also often means a puzzle might not give you clues on where to look next. In general, I'm not a big fan of that, but sometimes I do give in to the temptation for wacky puzzles.

I'm pretty sure the "<3" rows are intended. All the love for the solvers.

In the Greek round, every puzzle is themed after a Greek letter. The theme is meant to appear in the puzzle itself; it's not necessary for the theme to appear in the genre. For zeta, perhaps the most common use in mathematics is the Riemann zeta function, which is basically the sum 1/1^s + 1/2^s + 1/3^s + 1/4^s + …. (Strictly speaking, the definition is this for Re(s) > 1, and it's analytically extended to the complex plane. If that doesn't make sense to you, don't worry, I don't fully understand it either as it's out of my field.) It is an extremely important function in number theory, and the question on when it achieves a value of zero carries a bounty of one million dollars.

I decided to make use of this theme by taking a very mathematical genre, Arithmetic Box. Because the zeta function involves adding up fractions, I used fractions as the numbers. Since the major open question involves finding its zeroes, I made sure to include several equations, including an "equals to 0". (The only inequality is a trivial one, just to say "you're not getting any info from this".)

The typesetting of this puzzle was a nightmare, because Penpa isn't very good when it comes to more freestyle placement of things. I think this presentation is acceptable.

The Toketa? book series contains a lot of puzzles; they are written by Japanese authors as well as Serkan Yürekli. They also have puzzle articles, explaining some theory behind certain genres. Some of the books include an in-depth theory on Arrows. The results and theorems are pretty cursed.

The break-in for this puzzle uses one such result. I don't know if this particular one appeared in Toketa — I think it's fairly simple, all things considered, so it might be an earlier result. But it's still not obvious or trivial by any means.

Hint

Consider the clues on R1C2, R2C5, R4C1, and R5C2 (marked red in the above image). Each arrow next to a corner (marked green) must point to exactly one red square. The sum of the red squares is 8, so that's everything accounted for. All the other arrows cannot point to any red square. In particular, the middle arrow on each side (marked blue) must point straight to the center, as indicated.

If you're still having trouble after this, look at row 1, in particular R1C2 and R1C3.

You would think a puzzle with 40% fewer cells than expected of its size would be significantly easier. Hah. I stared at this puzzle for like an hour before I finally found the light.

Hint

Look at R2C3 (number marked in red) and R5C4 (number marked in blue). Each of these cells have 4 arrows potentially pointing to it (the other cells in red and blue). However, 1 cell is shared (colored purple), so in total, there are 7 arrows potentially pointing to R2C3 and R5C4 combined. Also note that no arrow can point to both numbers, so each arrow can count at most once to the sum of R2C3 and R5C4.

Now consider R2C4 (green). Arrows in row 2 that point to R2C3 must necessarily point to R2C4 too. Arrows in column 4 that point to R5C4 must necessarily point to R2C4 as well. That means, among the 4 arrows in row 2 and column 4, only 2 of them can point to R2C3/R5C4, due to R2C4. So we lose 2 arrows, leaving only 5. That means we have equality. In this case, equality means the arrow above column 3 must point to R2C3, and the arrow to the up-right of R5C4 must point to it, otherwise we don't have enough arrows to cover them. These are drawn on the image as indicated.

The top arrow is the important one, since now R1C2 is maximal.

Arrows puzzles on unusual grids are fascinating. Even when the grid is only changed slightly, the solve feels very different and foreign. I'm guessing it's because there are different lines of sight and different overlapping arrows.

Hint

Look at the central 6 (marked in blue), and compare it with R2C2 and R4C3 (marked in red) next to it. Considering the central 6, arrows in the main diagonal will also point to R2C2, and arrows in column 3 will also point to R4C3. However, the arrow at the left of row 4 (marked in green) must point to one of the red cells. Therefore, among the 4 potential arrows passing R2C2 and R4C3, at most 2 of them can point to the central 6. So the other 4 potential arrows to the central 6 must do so, as indicated.

If you're still having trouble, look at R1C2, and don't forget R2C2 is pretty busy with the central 6.

Usual Arrows puzzles take place in a square grid, where every line of sight has two potential arrows or none. A rectangular grid changes this by making some lines have only one potential arrow.

But obviously the big draw of this puzzle is its antisymmetry: every 3 is paired with a 4 in its rotationally symmetric spot. What, you didn't spot it until I said so? That's fair, it's a subtle theme. But it's striking, don't you agree?

Hint

Consider the clues on R1C2, R2C5, R3C3, and R4C1 (marked in red). No arrow can point to two of them, and two of the potential arrows (marked in blue) miss them entirely. But these clues add up to 16, and there are 16 remaining potential arrows, so every single one of them must point to one of these cells. In particular, 7 of the arrows (marked in green) only have one direction that point to one of these cells and so can be filled in, as indicated.

Obviously, after experimenting with grids that still roughly resemble usual Arrows puzzles, I decided to go wild. This grid feels incredibly weird; it barely feels like an Arrows puzzle. There aren't even any diagonal arrows! Okay, that's a mild spoiler, but it's straightforward once you study the grid; all diagonal directions point to more white cells, no grays in sight.

Hint

Consider the clues on the outside border (marked in red). They add up to 23. Now consider the corners, along with the white cells on R2,4,6C2,4,6 (all marked in green). The corners must point to exactly 3 red clues each, and the inner ones must point to exactly 1 each, so that accounts for 21.

The remaining white cells along the border (marked in blue) can only point to 2 red clues, so at least 6 of them must point into the interior of the grid. However, row 3 and column 3 can only support 1 arrow each. Therefore the other arrows (row 5 and column 5) are maximal and must point inside, as indicated.

If you're still having trouble, look at R4C2 next.

And here comes the variants. I don't actually know any Arrows variants, so each one of these was new to me and I was exploring the genre as I churned out puzzles. (That might be the reason why I burned out; exploring a genre is a tough job.)

Hint

The first step is to consider R3C3 (number marked red). Vertically, due to R1C3 (green number on top), there are at most 2 arrows pointing along this column, even counting the weights. So horizontally, there must be at least 3 arrows. Therefore, we need both arrows on row 3 to point horizontally, otherwise even a weighted arrow is not enough to count for 3. This is indicated with the arrows on red squares.

Next, we consider the same R3C3, along with the arrow to the left of row 1 (pink). Note that the pink arrow points to one of R1C3 and R3C2 (green). The 5 arrows that point to R3C3 also point to either R1C3 or R3C2, too. So in total, there are 6 arrows pointing to R1C3 and R3C2 already, which means all other arrows cannot point to either of these. This places 4 arrows, indicated as arrows on white cells.

Now, look at R1C4 (red number). Among its potential arrows, 4 of them are already pointing elsewhere due to the previous argument. There are 4 more arrows: 1 horizontally (pink), 2 vertically (blue), and 1 diagonally (red). However, the horizontal arrow can only count 1 due to R1C2 (green number on top). For the vertical arrows, R5C4 (green number on bottom) has clue 3, but it already counts once due to the arrow on its row (green arrow on bottom-left). Therefore, the vertical arrows to R1C4 can only count 2, even with the weights. So the diagonal arrow must contribute to the count; this is indicated by the red cell getting an arrow pointing to R1C4.

But we can actually say more. Consider the horizontal arrow (pink). If it didn't point to the 4, then it would point to R5C4 (green number on bottom). So not only the horizontal arrow wouldn't count, but it also would rob one of the vertical arrows! Then the 4 would get 0 from horizontal, at most 1 from vertical, and at most 2 from diagonal (if the red arrow is weighted). This is not enough. So the horizontal arrow must point to the 4; this is indicated by the pink cell getting an arrow pointing to R1C4.

This arrow is the most important one in the solve, since now everything should fall into place much more easily. If you're still having trouble, go back to the central 5 in R3C3, and note that the 2 in R1C3 now has 1 arrow counted already.

Compared to the previous six puzzles, I think this one feels more mellow. Low numbers everywhere, even including several 0's. Most arrows have very few possibilities remaining! Of course, one of the possibilities is always "this is the empty cell", so it's not as straightforward, but I think it's somewhat easier than the previous ones.

The puzzle, as it was posted on Twitter, was not unique. Oops! I have changed it for this archive. Read my thoughts below for the more complete reason.

Hint

It should be straightforward to place two arrows on the right of rows 1–2 (arrows on white cells). It is also helpful to mark numbers that are now full; these are indicated as darker gray cells above.

Now, there are 7 cells (green) along the top, left, and bottom sides whose potential directions all point to either R3C2 or R5C1 (red). But R3C2 and R5C1 add up to 4, so 3 of the arrows must be missing. This is exact, so the rest of the arrows on these sides are not empty. In particular, the arrow above column 4 (blue) is not empty, and so must point bottom-left, as indicated.

If you're still having trouble, note that R2C2 is now full, and that affects things on the bottom side.

The dashed circles are mainly to highlight the numbers, in case colors alone are not enough.

I'm pretty sure I came up with this variant following [2019-04-AprArr-06] and [2019-04-AprArr-07]. In those two puzzles, one cell from each side acts differently. So this one is the same. The main question was just, what would be a fun "acts differently" thing?

In a way, spotlight very naturally falls from there. The arrow does "something different" to the clues it hits: it makes the clues say, hey, we're different. Easy.

Hint

Consider R3C2 (purple) and R5C5 (red). There are 3 arrows (green) that must point to at least one of these: both on column 5, plus to the left of row 5. Since we now have the correct count, none of the other arrows may point to either R3C2 or R5C5.

The main implication is that the arrows in column 2 cannot point straight down. That means, the four clues in column 2 (blue and purple) must be hit by spotlight arrows, but each spotlight arrow can only hit one of them. So all 4 spotlights must hit these clues. In particular, the spotlights from the right side and bottom side (blue with arrow) can be fully determined, taking into account that they may not hit the black numbers. These are indicated with arrows on blue cells.

Welcome to scanning hell. Welcome to typesetting hell. This puzzle is horrifying.

Logically, the puzzle is actually much, much easier than the previous ones. I think I managed by considering at most two clues together, usually those that happen to overlap in two arrow cells so that their sum becomes maximal. (The first instance is R2C2 and R2C5, if you're wondering. Yes, they are the among the largest clues in the puzzle, so it's not too difficult to see. There's another instance in R1C1 and R5C5, which is a pretty wild pair.)

The main problem is the scanning. There are two layers of arrows, and the directions are absolutely disgusting. Hope you didn't miss marking any cell with your arrows!

Typesetting this on Penpa is also terrible. At first I used QWER/ASDF, which is, like, fine if I have to use 1-letter notation, but it's really not optimal. I thought about using 3 letters (NNE instead of Ne), but ultimately decided 2 letters was fine. It helps making the text not too squished, you don't really want to use Number → S size.

In theory this variant sounded interesting. In practice? Scanning hell, nope. I'm not doing this again.

After variants where I put one special arrow on each side, now we have a variant where I put one special object in the grid.

Note that the puzzle is almost completely symmetric: only R3C2 and R3C4 are different.

The puzzle, as it was posted on Twitter, was not unique. Oops! I have changed it for this archive. Read my thoughts below for the more complete reason.

Hint

Consider the clues on R1C2, R2C5, R3C3, R4C1, R5C4 (marked red), and the arrows at the ends of rows 1/3/5 and columns 1/3/5 (marked green). Each arrow must point to exactly one of the clues, but there are 12 arrows and only a sum of 9 from the clues. So there must be a black hole that blocks at least 3 arrows. The possible locations are indicated with blue circles. Also further note that all these locations block exactly 3 arrows, so all the remaining arrows must point to one of these clues.

However, only one of them actually works:

R3C2 and R3C4 (red) don't work because we know the black hole blocks at least 3 arrows, and so needs a clue of at least 3.

R1C4, R2C3, R4C3, and R5C2 (blue) don't work. To see this, look at the central 3. If the black hole is not on the central 3 itself, any horizontal arrow that points to (and counts for) the central 3 must also point to the 1 on R3C4, so there is at most 1 such horizontal arrow. So it needs 2 vertical arrows, i.e. the arrows in column 3 must point to the center. But a black hole in any of these locations will break this.

R4C5 (orange) doesn't work, although seeing this requires a little lookahead. Look at R2C5 (orange number). As mentioned previously, this clue must be fully pointed by arrows that we discussed earlier (marked in yellow). But if R4C5 was the black hole, then 5 of the 6 arrows don't work. The one to its bottom-right is busy pointing at the black hole. The one below it is blocked by the black hole. The ones to its top-left must point down to the central 3. The ones diagonally to bottom-left and top-right cannot point to the clue, because R3C4 is full from the central 3. So there aren't enough clues to point at the clue, so R4C5 cannot be the black hole.

As such, R2C1 (green) is the black hole, and this forces the 3 arrows (white) that get blocked by the black hole.

This variant actually sounds really natural. It's surprising it took me this long to think about it. You have numbers as clues, just do arithmetic on them. This Pair Sum, but also greater-than inequalities, XV variant like in Sudoku… In fact, you can simply take many Sudoku variants and they can probably work.

Hint

Consider R4C1 and R5C1 (red). Using the pair sums nearby, we can conclude these add up to 2. Now, the arrow to the left of row 5 (marked green) points to at least 1 of these, so we're only missing 1 more. Thus the arrows in column 1 (marked blue) cannot point along the column, since each one would contribute 2 to the sum, pointing both R4C1 and R5C1. So they must point away, as indicated. I have also added the current counts.

Now consider R2C1 and R2C3 (red). Using the pair sums, we conclude these must differ by 3, and R2C1 must be larger. Since R2C3 already counts 1 from the previous deduction, it follows R2C1 must be at least 4. But among the arrows that point to R2C1, there are only 4 (marked green) that do not also point at R2C3. (The arrows along row 2 point to R2C1, but also to R2C3, meaning their difference wouldn't change.) Therefore these 4 arrows must all point to R2C1. Moreover, among the arrows (blue) that might point to R2C3 but not R2C1, none of them can do so, which lets us fill in a few more arrows, as indicated.

If you're still having trouble, note that R5C1 now counts 2.

The variant "one of these is different" continues!

The puzzle, as it was posted on Twitter, was not unique. Oops! I actually posted an original version of the puzzle on Twitter, it was not unique, I posted a fix, and only now I realized it was also not unique. I have changed it for this archive. Read my thoughts below for the more complete reason.

Hint

First, note the 0's on R3C2 and R5C2 (red). These block the arrow to the left of row 5 (red), so one of them must be lying. In particular, the 3 in R2C2 (blue number) is truthful.

Now consider that 3. It is truthful, but also one of the 0's earlier is truthful. So there is no arrow along column 2. So it has 4 potential arrows remaining. So there is at least 1 arrow along the diagonal. This points to the 1 in R3C1 (blue number).

Finally, consider the arrow below column 1 (green). It points to either R3C1 (the blue 1) or R5C2 (the lower red 0). One of them must thus be lying, which means R3C2 (the upper red 0) is truthful. This places 4 arrows near corners to avoid the 0 (indicated in the next picture). Furthermore, because R3C2 is truthful, R5C2 is lying (indicated as dark gray in the next picture).

Note that the 4 arrows cause the 3 on R5C5 to be full.

Now consider R4C2 (red) and R5C1 (blue). For R4C2, the 0 in R3C2 causes there to be 4 potential arrows remaining, horizontally (red and purple) and diagonally (green). For R5C1, the fact that R5C5 is full causes there to be 4 potential arrows remaining, diagonally (blue and purple) and vertically (green). Each of these clues need 2 more arrows. However, the candidates overlap on one square (purple).

Therefore, there is at least 1 arrow that is on a green cell. All of these green arrows point to R3C1 (green), so it counts at least 1 arrow here. But it already counts 1 more arrow from R2C2. Therefore R3C1 is a liar. This means R3C5 is truthful and thus is full, and the solve goes from there.

I burned out from writing for the series after [2019-04-AprArr-12]. The series had been filled with tough puzzles, but that also meant constructing them was very difficult and time-consuming.

I did manage to write this puzzle, probably during the two weeks of my series, hoping to release it at another time when I had a suitable variant theming on the days around me. Note how [2019-04-AprArr-06] (Weighted) until [2019-04-AprArr-08] (Spotlight) were themed, "one arrow on each side is different". The other variants didn't really follow a theme, though, so not sure why I was waiting.

Either way, I released the puzzle as a bonus puzzle. I think it was the 26th of the month, but it was the 13th puzzle and it will be numbered 13 in this archive.

Unlike the other entries in this series, I don't include hints for this puzzle. I think this is comparatively much, much easier than the previous ones, and it shouldn't be too difficult to solve.

Since part of the "hindsight" round is revisiting past genres, this is one of them. The genre originally appeared in 18th 24HPC Round 5, written by Nikola Živanović.

Battleships with a standard fleet normally take place on a 10×10 grid to give some room. But some variants, such as Retrograde Battleships and this, don't have particularly strong clues, and putting them on a packed grid is the main way to make good logic.

I don't know if this variant has too much potential, but I think of this as more a gimmick variant that is fun and novel for several puzzles.

Bunnyhop is an inherently confusing genre. I tried to construct a puzzle that's relatively tame, but it ended up being difficult anyway. It's not easy to figure out where to break into the puzzle. (Tip: Three of the corners all have the same local deduction. The break-in is in the last one.)

With only two kinds of clues (white cell and black cell) that are total (the absence of a "clue", here a black cell, is also meaningful), it is pretty hard to force in any particular aesthetic design. Here I went with some Y patterns, although one was upside down and two had an extra cell each. But overall, I'm still pleased with this puzzle.

If you missed it, this puzzle was chosen as a puzzle in the finals of the championship, because it's one of the most beautiful puzzles the testers have seen. Yay!

I tried to put in a global deduction in the puzzle. The puzzle unfortunately had to be big to fit in the deduction, but I do think it's gorgeous.

Hint

Broadly speaking, the puzzle can be divided into four areas: central (red), top-left (yellow), bottom-left (green), and right (blue). There is only 1 entrance between each pair of areas, which means each area only has 3 entrances in total. So the loop must visit each area in turn and clean up everything in there before going to the next area.

The central area is the one we're interested in. Color its vertices in a checkerboard pattern (here using small circles). All entrances to the area are "diagonal", so they must visit a vertex of a particular parity: the exits to yellow and to green have the white parity, while the exit to blue has the black parity.

Finally, the central area has 20 cells to be visited, so the loop has length exactly 20 in the central area. That means the loop must enter and exit the central area on the same parity. Therefore, the loop uses the exits to yellow and green, and not the one to blue. More importantly, the yellow-green exit is not used, and that allows drawing a big chunk of the loop in the yellow and green areas.

I'm guessing I wrote this because I was curious of a Castle Wall with entirely black clues. The resulting break-in is pretty funny. I think I was having trouble making the rest of the puzzle unique, though.

Themeless, pretty straightforward. However, I think this was my first ever Cave and I was trying to feel how the genre worked.

The theme is cute, a "7" made of 7s. Unfortunately there are nine 7s to write that shape. I propose swapping the glyphs for 7 and 9 just so this theme can work out even better.

Anyway, I don't remember why I wrote this. Maybe I was just feeling like it. Not at all a bad reason to write a logic puzzle though, surely?

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

I created this genre because I wanted to find a genre that was simple to explain, and yet would still be something new and unusual. I decided this "counting neighbors" idea was pretty novel.

I've written a few Contact puzzles before this, although I'll have to compile them later. This one was written when someone suggested about making a puzzle set of introductory puzzles to certain genres. I agreed that it would be nice, but... did it have to be a "set"? So this puzzle came out.

Although big, it's designed to be solved very smoothly in gradually increasing difficulty, as you make your way from the top-left corner and follow the path.

Yes, the puzzle is 7×6. I mean, I need a grid with even size. I didn't go with 7×7 with a missing square, because the missing square itself might lead to weird things in Contact. And 8×8 is too large.

I haven't quite gotten the hang of seeding in aesthetic themes in Contact, but I think this is a decent one. All those increasing sequences forming the letter H.

A large puzzle, a small number of givens. Turns out the puzzle is surprisingly pretty easy, with most of the solve being derived by the domino tiling. I suspect I want a hexagonal grid for Contact puzzles in general. That said, this puzzle does highlight one pattern in Contact that I like.

It's antisymmetric! Each 1 is opposite a 2. It's pretty, and the solve is pretty nice. The top and bottom edges have the same pattern but are offset, leading to different resolutions.

This puzzle wasn't part of the set, because the testers mistakenly thought there were multiple solutions and didn't contact me about it. Ugh. Well, this is the puzzle released publicly for the first time, then.

It's brutal. Not sure if in a good way, because there are some bifurcations needed. (And that might be part of the reason the testers got it wrong.) It does look pretty though, with the squares of 1/2/3 along the middle.

Although the theme of our rounds is "hindsight is 20/20", sometimes you just can't make use of that 0. In that case, time to fall back to the trusty 24 theme.

In the Greek round, every puzzle is themed after a Greek letter. The theme is meant to appear in the puzzle itself; it's not necessary for the theme to appear in the genre. Mu is a fairly popular letter; for example, it is used for the SI prefix micro and the Möbius function. But for whatever reason, I couldn't come up with a good theme based on these.

I love the game Zendo; I think it's a genius implementation of inductive logic as a game. Kory Heath, the designer, named the game after the Japanese meditation hall, and in general involved terminology of Buddhism meditation. This is when I saw the term "mu". It essentially means "unask the question"; it's pointing out that the premise of a question is flawed. In the game, part of the game is to guess a hidden rule by stating a rule of your own. Sometimes, a rule is ambiguous — in "the largest piece is green", what if there are multiple pieces of the same largest size? — and "mu" is the only reasonable reply, pointing out such ambiguity so the player can state their rule better.

I imagined this connection as a theme, using a lot of question mark clues in a puzzle so that the solver could "unask the question" and deduce these question marks were all determined in the first place. If you think it's quite far-fetched, I agree, it does feel like a weak connection. But I only needed a little spark to start writing a puzzle. Making this connection led me to Cross the Streams, a genre with naturally a lot of question marks. Putting the theme clues at the top made me explore what the implications would be, and I think the break-in for this puzzle is pretty neat. I wouldn't have come up with this logic if I didn't have anything to start playing around with.

In the contest, which was themed after the seven sins, this was named "Sum Sandwich" for the Greed sin. It followed a genre named Ham Sandwich, which was basically Doppelblock with number set {0,0,1,1,1,1}.

I don't think this has any aesthetic theme whatsoever, it's likely driven by logical steps I tried to put in.

As part of the "20/20" round themed after 20s and doubles, this genre has "double" in its name and so is suitable for our theme. (Well, that, and the genre itself does have two of something.)

When you get really used to the usual norm in logic puzzles, it feels really foreign to have it broken. For example, if a loop can cross itself, you no longer trust basic deductions you would otherwise make by instinct. This feels similar, given that you're drawing two loops and not one, although it finds solace in that "normal" cells still behave mostly normal. It's a genre that messes with the brain, but it's pretty fun.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

How on earth did I think of Ebony & Ivory? I probably looked Janko's puzzle archive. (Eric's puzzle rules doc didn't exist then.) E is a difficult letter, and I'll take whatever I can get. On retrospect, Easy As ABC might lead to interesting ideas, but the definition of abacus will have to be modified for it (probably simply reading letters, disregarding empty spaces).

Also, Ebony & Ivory is a very weird genre; it seems so hard to force anything whatsoever.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

Turns out that the Yajilin-like clause with the loop ends up driving a lot of the puzzle. I think Ebony & Ivory should come with some sort of variant (e.g. wall, coral, loop) to become an interesting puzzle.

I'm also hitting the limits of Penpa that I know. I wish I could show the abacus lines better, but unfortunately you'll have to live with this for now. Maybe if I figure out a new trick in the future.

The theme of the puzzle is quite nice: prime numbers. However, my young self focused on the wrong thing. The puzzle uses few givens, so I thought it would be incredibly hard. As a comment pointed out, you can very easily make a 10×10 Fillomino with 1% given cells. Of course, it wouldn't be interesting.

Either way, whatever my foolish self was thinking, this puzzle is still pretty nice, with an interesting finish.

This puzzle was submitted for Logicsmith Exhibition 5, a competition ran by Grant Fikes where people would submit puzzles and then vote for their favorites. The theme was a Fillomino, in which there were exactly 36 givens: each digit 1–9 should appear exactly 4 times each. (The layout of the givens should also be rotationally symmetric.)

According to his comments, "the first 40% was easy, but then the difficulty increased somewhat jarringly". (Which is true, after I tried solving it again before including it here in the archive.) I'll just chalk it up to me being very new to puzzle writing at that time.

Am I proud of the puzzle? For something I wrote very early in my puzzling journey, very much so. Nowadays I would make the start different, although I know it would likely lead to a completely different puzzle. But still, in a way, this shows I can write an easy puzzle and also a hard puzzle.

Since this was part of WAPC, I was looking for genres to show about myself. Well, I love Fillomino, so I figured I could include one. And since it's about showing myself, what's better than spelling my name?

As a puzzle, it's relatively easy with a nice, smooth solve. Nothing too remarkable, but that's perfectly fine, it can simply be something familiar for solvers.

In Puzzlers Club, I once did a "livestream" of my thought process as I constructed a puzzle. It mostly turned into an incoherent rambling where I posted a bunch of images with little annotation. But this is the resulting puzzle, and it's quite nice.

When writing a Fillomino without any particular prompt, I feel like I default to some sort of square ring pattern that doesn't touch the border, like [2019-10-14] above. This one has an additional theme on top of it, with all the 2×2 checkerboard patterns.

If anything caught my eye about the aesthetic, it's the middle. I think it makes sense; putting a whole extra 2×2 makes the grid too stuffed and it's probably too easy to see regions blocking each other, and leaving it empty makes a giant 4×4 hole that might be difficult to force unique. But I could probably have done another try on the puzzle that removed the center, probably at the expense of introducing some larger numbers.

This puzzle is probably my first ever "commissioned" logic puzzle. This was published in Puzzler's Bulletin 17, a weekly series of puzzles curated by Tawan Sunathvanichkul as part of his TamBox series.

Tawan contacted me on whether I wanted to write a puzzle for his series. At this time, I was quite rusty and rarely wrote any puzzle, so I decided to say yes just so I had more practice. Since Fillomino was my favorite genre, I decided to write one. Initially I only put the givens in those locations without the additional aesthetic theme. Midway through writing, I noticed I had several rings of 1-6, and decided to extend it as the theme for the whole puzzle. It might not have been the wisest idea; the ending became somewhat unwieldy. Despite that, I'm still very satisfied with the puzzle. (And yes, I got paid for it.)

Make sure to check out the TamBox series (whether Puzzler's Bulletins or the paid PULZE issues) for more good puzzles! I haven't written any more for the series, though, as of issue 116.

In the Greek round, every puzzle is themed after a Greek letter. The theme is meant to appear in the puzzle itself; it's not necessary for the theme to appear in the genre.

One theme I was intrigued in was mathematical constants. A lot of constants are named after Greek letters, from the incredibly well-known π to more obscure ones. This is one of the latter.

The Euler–Mascheroni constant, denoted by γ, is a constant based on the relationship of the natural logarithm and the harmonic series. In brief, the harmonic series is bounded above and below by the integral of 1/x (which is simply the natural logarithm), and the Euler–Mascheroni constant measures the amount of error of this bound. Check out the Wikipedia article for more details.

This is one of the earliest puzzles written for the round, where we're not yet sure how the puzzles will look like for sure. So I decided to lead by example and present a puzzle themed in this manner. The Euler–Mascheroni constant, 0.5772156649…, appears along a curve at the bottom. The curve is also meant to resemble the reciprocal function 1/x; it keeps decaying closer and closer to zero, but its decay slows down over time. The rest of the puzzle was built on these as fixed givens.

At the end, most of the puzzles in the round were based more on having the Greek letter appear somewhere in the puzzle, instead of a more involved connection like this. I'm still happy with the puzzle, though.

Because the Greek round doesn't constrain the genre, I chose a genre I was very comfortable with. I really like Fillomino. It's pretty easy to embed a mathematical constant (as long as you don't have a 0, I guess). So it wasn't too difficult to write the puzzle, and it ended up having a pretty nice and varied logical path.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

Cipher is probably the most obvious way for an "ambiguous" theme. Cipher puzzles are generally difficult to typeset, though, because you need to write over the letter. Most people write the letter in a smaller form. I think I currently like making them white, so that they are readable before you write anything, but once you write something on them, they can be mostly ignored.

Turns out I'm already big on this Skymin theming back in 2013. The puzzle also ends up being quite silly, although with quite some effort in counting involved.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

I didn't remember this puzzle back then, but now that I did it (as I do when putting puzzles to the archive), and wow this puzzle feels so alien and bizarre. It's pretty quirky, and the theme is pretty silly — a little spoiler, but a straightforward observation at the beginning of the puzzle: you try extending the A's on all corners and they keep growing bigger. It does involve quite some counting, though; I guess past me was very comfortable with heavy counting. It's still a worthwhile puzzle to try.

Variant rules: Fillomino rules. However, there is one hidden rule that causes some Fillomino solutions to be valid while others aren't. An example puzzle, with its unique valid solution and an invalid solution, is given to you above. The solutions may have additional markings to help you. Determine the hidden rule and solve the puzzle following that rule.

Since an "aha moment" is not quite deductive logic, you might prefer to bypass it. If you wish to skip the aha moment and want to simply find out the hidden rule, click the spoiler below.

Hidden rule for this puzzle

Sentry Fillomino: In each row/column, all instances of any specific number must belong to the same region. Note that they might not be contiguous, as long as they belong to the same region; see the first column.

The inspiration to put "Mysterious" puzzles comes from Allied Occupation, a hunt puzzle where there are Fillomino puzzles with hidden rules you also have to figure out. I think Fillomino is incredibly versatile and there are many ways to add new fun rules. But Mysterious variants are generally tricky, because I can only hope I designed the example well enough. No way around it, since it's not something that can be deduced.

When invited to help with this hunt puzzle, I started thinking of genres, seeing if a little change to the rules could make it feel truly cursed. This is one I ended up with, and I'm proud of all the unhinged logic that comes out from it.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

Fuzuli seems to be a pretty niche genre, so I was quite surprised when I was assigned to write this. At the same time, it has a lot of similarities in structure with Doppelblock: it's Latin square except some cells are empty.

I decided to approach this puzzle in the way I know best: put in some high-level deduction as the key step, and the rest of the puzzle basically falls into place. I think I'm particularly proud of said key step in this puzzle, even if it requires some mathematical proof to formalize.

Also, this round is pretty funny. It has 11 puzzles and is worth a total of 850 points. Four puzzles are all tied at 105 points apiece, this being one of them. Pick your poison?

I don't remember if there's any specific reason I decided to write a Gaps puzzle (called Gappy Blocks in the set). But given the 3 theme, I must have played around with the arrangement that made it as the break-in, and realized its power. Honestly I forgot about this puzzle, but now that I've put it to the archive, I'm quite proud of it. The solve path is quite fascinating, reminiscent of some unusual deductions in Star Battle.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

I don't know why I chose Gaps as a genre for this. First of all, Gaps is, strictly speaking, an object placement genre; my rules here even write that you're placing "stars" rather than black cells. Second, given that black cells can't touch, this just says the count of stars on the lines are the same, possibly with multiplicity issues if a cell is counted multiple times.

That said, formulating it as black cells makes the variant [2017-12-TGA-4] below easier to state, and it gets to actually have adjacent black cells for the abacus.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

The good news is that this variant adds new possibilities to the abacus lines, since now it may read a segment of 1 or 2. (Or 3?) The bad news is that the rules get really convoluted. Gaps (Domino) in general feels like a bizarre thing, and now I'm adding another weird variant to it too.

This was the first appearance of this genre, ever, anywhere. The story is pretty interesting; read all about it.

As the first ever Greener Grasses puzzle, this plays it relatively safe, using some of the techniques we found while constructing the puzzle.

When constructing Greener Grasses puzzles, I find myself falling back to regions of size 3. I think it's the sweet spot, with 2 being too small and 4 being too large. (Although others have managed to construct puzzles with different region sizes.)

This puzzle plays it safe and easy, without anything too remarkable, but that's perfectly fine.

The density of clues in a Greener Grasses puzzle affects the solve strongly. On one hand, you can have sparse clues; then every region can only have 1 or so, and the puzzle is more about making sure every cell finds a symbol and equal-symbol regions aren't adjacent. On the other hand, you can have "oops all clues", and the subset part of the ruleset doesn't matter, you just need regions to not have the exact same contents. You can also have anywhere within the spectrum and the feel of the puzzle changes.

Obviously, this puzzle is all the way on the "oops all clues" side. I was curious how it would work, and I must say I'm fascinated, it's a very different feel. It does become somewhat harder to spot where to break in, but coloring the O's helps giving a visual.

I would later use the same theme in [2024-04-24HPC12-22] below.

In the Zodiac round, every puzzle is themed after either one of the animals in the Chinese/Eastern zodiac, or one of the constellations in the astrological/western zodiac. There were two goats: one in the Chinese zodiac, one as Capricorn in the astrological zodiac. We weren't sure how to distinguish them, so at that point, we just took ideas which could go either way. We had Yagit (also known as Goats & Wolves) on file, and someone suggested Greener Grasses (because goats eat grass) which I was intrigued by.

Capricorn had an actual symbol, though. There could be a stronger theming from the puzzle itself. At first I meddled with Yagit where the givens formed a specific symbol. For whatever reason, I stuck with the old symbol of Capricorn instead of the new symbol that's present in Unicode. I didn't get anywhere, mainly because I had no idea how to solve or write Yagit puzzles. So I turned to Greener Grasses. (yyao would later pick up the Yagit idea to put it as the goat puzzle in Chinese zodiac.)

At first, I tried an arrangement of givens in the Capricorn symbol just like before. But I noticed a pretty big empty space at the top-left of the symbol. That wouldn't work without givens, so I thought of another way. What if I did a repeat of [2020-11-25Y-22], where every single cell had a given of one of two letters? Would I be able to have the clues of one particular letter resemble the Capricorn symbol (and the other would be the "background color")? I tried the top-left area, and it resolved largely uniquely, so I decided to go with it.

Of course, simply copying the symbol wouldn't do; there was very little chance the puzzle would be unique. I had to make some tweaks to the symbol, and I think the right half is slightly scuffed as a result. But I got it working, and I'm pretty proud of the aesthetics. The logic suffered slightly — there's quite a bit more look-ahead and bifurcation than I wanted — but I think it's a fine compromise.

Finally, I realized the rules of Greener Grasses didn't require the symbols to be letters. So I got cute and put in emojis.

Update: Penpa is constantly being updated, and I suppose at some point, the font to display emojis got changed. I think this design is still readable enough, though.

Puzzlers Club has a series of events called "Logic Showcase", where people are invited to write a logic puzzle based on a particular prompt, then the puzzles are published and people vote for their favorites. (See [2024-06-12] Turnaround (Abacus) for another puzzle I wrote for such event.)

In this particular installment of Logic Showcase, the prompt is simply to write a Haisu puzzle. I decided to write this one. I intentionally kept it pretty simple; Haisu is a challenging genre in general, and I believe even a 7×7 can be pretty difficult already. (That said, I also tried to minimize lookahead.)

More importantly, I'm incredibly proud of the aesthetic theme. All the regions and givens are symmetric, except obviously for swapping S and G, but the solve is not similar at all; I don't even think you can say there are two halves to the puzzle. The regions are all rectangles, which feels clean.

Ultimately, I won the showcase with this entry. There are some talented constructors in Puzzlers Club that went far and beyond; I believe there was an entry that was 29×29 and had a "107" on the grid. In a sense, my entry was one of the easiest. But that also means it was one of the most approachable, so people particularly liked it. The aesthetic most certainly helped.

Since part of the "hindsight" round is revisiting past genres, this is one of them. We couldn't resist making a throwback to our own rounds; this genre previously appeared in 19th 24HPC Round 11, written by Puzzlers Club.

This puzzle is actually valued fairly low, but I was struggling to find a clean logical solution. A lot of Haisu puzzles can be solved with intuition, not unlike Numberlink and such, so that might have been why it was valued low.

Like [2020-05-23] above, this was also an entry for some installment of a Logic Showcase. The prompt was "foreshadowing clues", where a clue would only "happen" some time later along the solution. For example, given a directed loop, a clue might say something is true N cells later along the loop.

I had the idea of combining this with Haisu. At first, I actually took this more broadly; the foreshadowing didn't have to be a specific number. So I was thinking of "the next region the path visits is the N-th visit", in the same vein of a puzzle genre called Remembered Length. But the rules of the showcase seemed to forbid it, because clues "should also indicate the distance" to when they happen. So I modified it in the obvious way: a clue only takes place this many cells later.

I could have gone a more general route: each Haisu clue could have an independent number indicating when it would happen. For example, I might say "Haisu clue 3 will happen 5 cells from now". But I decided merging the two numbers was cleaner and more impressive.

I also recognized the possibility of a question mark clue (?), due to merging these two quantities. Either Haisu clue 1 will happen 1 cell from now, or Haisu clue 2 will happen 2 cells from now, or 3 in 3 cells, and so on. But when I tried it, I was getting a lot of ? = 1; it was the easiest to satisfy. So I decided not to pursue it for this showcase. Maybe in the future.

I actually posted this puzzle here on this archive before the showcase ended. I realized I didn't really want to bother with the competitive aspect; the showcase is just a reason for me to write puzzles. Turns out my puzzle got 3rd place out of 8, with 3 votes (the top puzzle got 4 votes). I'm satisfied enough with that. With how some showcases lean toward incredibly difficult entries, I try to pitch a reasonable one every so often that is nevertheless still delightful.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

But wait, this puzzle doesn't even appear on the puzzle page for Polyglot! Well, uh, you'll figure it out. Read the solution page for Polyglot for more info.

The "almost unique" variant is inspired by Something is Off, a hunt puzzle where each puzzle has two solutions (in many cases simply due to symmetry). I figured it's a silly idea to present a puzzle that's symmetrical, but the solution clearly can't be; but as it turns out, once you break symmetry one way or another, the rest of the puzzle is unique.

On retrospect, it's a really dumb idea. It might be interesting in theory, but it just sticks out as a sore thumb, even when you can explicitly tell where you break the symmetry.

In addition to the issues I mentioned previously in [2020-11-25Y-19], to make matters worse, Penpa doesn't support "almost unique" variants cleanly; it assumes all logic puzzles have one solution, after all. When this appeared in the contest, I asked LMI to accept both possible answers for the answer key. (Multiple possible answers have been used before for alternative interpretations of the answer key; for example, when counting "lengths of segments", some people count center to center and some people count the number of cells used, which differ by 1. Usually LMI accepts both.) But I can't tell Penpa to do the same thing.

For RED SUS, I initially only contributed [2021-12-REDSUS-01] Fillomino (Suspicious). Then I tested the puzzles that lovemathboy wrote. I felt one of them (a Slitherlink) wasn't fun or cursed enough, and we decided to replace it. I also noticed there weren't enough region division puzzles, so I wrote one such puzzle. I don't know why my thought led to Heteromino, as it's a relatively unknown genre, but its rules are certainly simple and yet easy to play with.

When I was adding this puzzle to this archive, I had to solve it again, and somehow I was struggling so hard. So I guess it's cursed enough? More likely is just I missed several deductions that should have been clear.

Okay, this is a bit awkward. I looked at this puzzle when putting it to this archive, and tried to solve it again, because of course. And I don't actually remember the solution path; I was struggling to solve it again. (To be fair, the point value might have reflected this; it was 27 points when puzzles in the earlier half were in the 10-20 range.) I still don't know what I was thinking. River theory helps with this puzzle (although not that much). But also, this was written in 2018, river theory was much later. Could I have bifurcated a whole lot?

Aesthetically, this is a pretty silly puzzle. I'm pretty sure I came up with the top-left region and the bottom "river" separately and put them together. The top-right half is rotationally symmetric by itself, which suggests I might have managed to come up with quite a lot of black squares but needed a few more to disambiguate, so I added borders where their counterparts were "useless".

Either way, it's still a puzzle in the set, however bizarre its history is.

I read up on a Twitter thread by @agnomy, which detailed a new theory in Heyawake. I then wrote up my own version in English, with this puzzle accompanying it. It started a whole new kind of Heyawake puzzles using this "penalty theory" technique. In addition, several people extended my work into better write-ups and guides: one by tckmn and one by Teal.

Some time before this, I had also come up with gridpoint counting argument for Nurikabe, which is a sort of "penalty" theory, accompanied with [2019-05-19] Nurikabe to illustrate it. In addition, there was also something called river theory for Heyawake. Penalty theory (for Heyawake), river theory, gridpoint counting argument; they are all based on deep mathematical theory embedded in logic puzzles, and it's so cool to discover them. I would later present some of them in Mathematics in Puzzles — originally an online talk in April 2024 presented in ThinkyCon (a conference for thinky puzzle game developers), later turned into an article in its own right.

I have no idea how I came up with this variant. I mean, it was in 2012, over a decade ago! That said, it seems that it was received well — Prasanna commented on my original blog post that it was a "wonderful variation". I think it's a combination of many things. The Minesweeper clues were likely inspired from Smullyanic Dynasty (which I used in Deception, see [2013-05-Deception-05] Smullyanic Dynasty). I also liked the ambiguity of whether a clue is Heyawake or Minesweeper; in particular, the "one is lying" aspect led to some tricky logic. Many years later, I would learn that Nikoli's Usowan was similar in some respects, most notably the "one is lying" aspect — and it also uses Minesweeper clues! — although I executed it differently.

I would later try different variations of the ruleset, and I wrote some puzzles using the new ruleset for Deception (see [2013-05-Deception-11]). On my blog post in 2013, I even called it "the final version" of the ruleset. Hahaha. It was ridiculously complicated, with two kinds of clues each having two possible meanings, and lost the charm of "one in each region is different". I came back to my senses and went back to this original ruleset when it appeared in 25 Years.

If you follow my blog from the olden days, you might notice that this puzzle is present here while other puzzles chronologically near this aren't in this archive yet. The main reason is so I can have the "real", current version of Surveyors Heyawake. I also consider this variation associated with myself strongly enough that it's not spelled "Heyawake (Surveyors)" like many variants, it's its own genre "Surveyors Heyawake". Behold, one of my earliest inventions.

The puzzle itself? It's tricky if you haven't had exposure to this variation before, but I tried putting a bunch of simpler tricks in there. I think it's a delight as you learn different ways these clues behave.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

What was I thinking with this ruleset? It's ugly. The original version of Surveyors Heyawake, as presented in [2012-04-07], had two clue types, and I think I liked the ambiguity enough to expand it in many ways. I dropped the condition that there's exactly one Heyawake clue, so every clue can be Heyawake or Minesweeper. I added outside clues with its own two new meanings. (Outside clues aren't in here, but they are in [2013-05-Deception-12].) The ruleset ballooned in size.

On retrospect, the "one clue is different" of Surveyors Heyawake is actually really pretty, and I should have held onto it. The outside clues were too much. That's why this ruleset is now called "prototype", as I have now abandoned this and gone back to the original.

The puzzle itself has a cute theme, though. The clues are all on the top-left of their regions, which wouldn't normally be surprising in Heyawake. But then you realize they can be Minseweeper clues, where the positioning very much matters. Although I wish I made the numbers completely symmetric to emphasize this theme even better.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

This particular prototype ruleset was only used in Deception; as explained in [2013-05-Deception-11], I later would revert this ruleset back to the original. So this and the previous puzzle are the only two puzzles with this ruleset. And this puzzle is the only one with outside clues. I still think having four meanings of clues is excessive, but Coral clues do have some interesting interactions with the Heyawake's signature "no line crossing two walls" rule, so that might be worth exploring independently.

Surveyors Heyawake appeared in Deception in a revised form, and let's say it's too... enthusiastic. I decided to go back to my roots here, with only clues inside the grid, and the guarantee that exactly one clue is a Heyawake clue in each region.

With a 7×7 grid that's divided into regions, I do often go to this layout; see also [2020-05-23] Haisu I wrote a few months before this one. It's a pretty reliable layout, though. It's pretty. I also managed to get in a square ring of givens, made entirely of 1s and 2s. It's just so pleasant to see.

I think 3×3 regions are a bit weird in this variant; a Minesweeper clue's "area of influence" is also 3×3, so it feels repetitive in some way. But at least none of the numbers is in the middle of a region.

I'm also not sure why I went with another square pattern after [2020-11-25Y-01] did, but I think this was executed differently. And the puzzle was a delight. It's tricky to find the break-in. The solve isn't straightforward after that either, but it's reasonably smooth and nice.

I tend to have weird thoughts during shower. One time, while I was showering, I thought of a wacky deduction that might be possible in Hidoku. The structure is similar to this puzzle: a main diagonal divides the puzzle into two halves connected with several "corridors", and I wanted to use up all these corridors by having the path to alternate sides often through the clues. This didn't quite materialize in this puzzle, but I think what I have is still pretty nice.

I don't remember what prompted me to write this puzzle, but it's definitely quite a silly variant. Doesn't mean easy, though; this has a logical path, but very narrow.

Since 2020 or so, I have been writing puzzles for specific purposes. Most of the time, it's to show off something can be done. For example, I made the genres Contact and Turnaround, so I wrote a few puzzles to showcase them. Often, this is inspired by some sort of discussion. [2023-08-26] Star Battle (Regionless) was written directly as a response of people liking the potential of 9×9 Regionless Star Battles.

This puzzle is the same. There was some discussion about Hitori and how the Nikoli version often had unnecessary clues — which is why many Hitori puzzles from other people nowadays remove them. I joked about a Hitori where all clues were lying, and that the rules were also lying, you simply have to Spheal on every cell. (Spheal is an in-joke in Puzzlers Club because it's very round and friend-shaped.) Then djmathman said, "hitori (knapp daneben) would be incredibly incredibly cursed".

Well, I thought about it and decided to write something. It is pretty cursed (and difficult), but I think it's a lot of fun.

While the other genres in the contest have a clear small puzzle and large puzzle, I think this and [2025-05-Serbia-08] below are roughly equal in difficulty. They are definitely the same size.

In fact, I think their logical steps are similar. I'm not sure whether it's due to Hit Points being a very new genre for me.

I think this slightly edges [2025-05-Serbia-07] above in terms of aesthetics, although both are pretty.

Why did I pick two 6×6 as my puzzles? I forgot. I definitely tried odd-size grids, because they have different properties (the middle number can be a fixed point for both directions), but I guess I didn't like any of them.

It's antisymmetric! I also like the "knight moves" pattern.

I actually made two small Isowatari puzzles. This one is the one I decided to send. The other one was very similar, but on a 7×7 with less clues. But it didn't quite manage to be antisymmetric, so I decided this one was better aesthetically.

I think this puzzle has an unusual opening even for an unusual genre like Isowatari. But it's really pretty with all the diagonal lines, and the logic was delightful.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

As a big Shaymin fan, I do like to feature the number 492. That might have been the only reason I wrote this puzzle. I just found it laying around on my Twitter puzzle account with no other reason.

This puzzle has an incredibly unfortunate aesthetic theme.

Now, I'm very proud of the various increasing sequences here. Every triplet of clues is an increasing consecutive sequence, it's delightful.

However, the puzzle seems to promise more. For the left side, the sequences (from bottom to top, equivalently from left to right) are 3-4-5, 4-5-6, 5-6-7. So not only is each sequence increasing, but the three sequences together are also increasing. But what about the right side? It's 6-7-8, 6-7-8, 7-8-9. That bottom sequence just begs to be 5-6-7.

Of course, I'm very sure I've tried to make it work, and eventually gave up. It still feels imperfect, you know.

Mark Rosewater is one of the lead designers of Magic: The Gathering, and I learned a lot of game design from his various articles. In GDC 2016, he gave a talk called "Twenty Years, Twenty Lessons"; it's not just applicable to Magic, it's applicable to virtually all of game design. And what are puzzles if not single-player games? One of the lessons he gave was, "aesthetics matter". Everything might line up so well, but just a single blemish is enough to draw attention to it, making it feel imperfect.

Now, not like the puzzle is bad; I'm still proud to have made the pattern, and the logic is nice and smooth. But I would try more to make 5-6-7 work. Alternately, I would scrap the second part of the pattern; I would just put six unrelated sequences, so that there's no greater "thing" that people would look for.

The abacus variant debuted in The Great Abacus, but I ultimately felt it could be executed better. In particular, the line didn't have to double back on itself, and giving the direction of the line helped reducing cases to keep track of. And so this particular variant ruleset was born.

In addition, the variant itself could be used for many kinds of shading puzzles. (Well, not dynasty ones.) So I decided to choose Kurotto for the test. The shading was particularly open without any structure to it.

One problem with the abacus variant in general, though, is that I haven't found a good way to typeset it. Right now I'm using thermometers, but they cover a good chunk of their cells. And on Penpa, shading goes below thermometer elements, so it becomes hard to read. I don't have a good idea here. Maybe construct the shapes using the Line and Shape elements (circles for the bulbs)? I also have since tried implementing abacus variants in other kinds, like in loop puzzles with [2024-06-12] Turnaround (Abacus Circles), and thermometers work much better for loops.

This puzzle itself isn't too special, but it's fun to fill the whole grid with abacus lines and see what happens. Note that the "cyclone" patterns are different along the diagonal.

[2020-11-25Y-13] above have short abacus lines, so the abacus variant doesn't come online much. These ones are much longer, and they still wrap the entire grid in them, so it's of utmost importance to figure out what the abacus lines are, quickly. But where can you start? That's the delight of the puzzle.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

Although I guess I wonder why I wrote three Masyu puzzles here.

Masyu puzzles have a particular aesthetic theme that, if it can be pulled off, look mind-blowing: anti-symmetric clues. The clues are rotationally symmetric, and each black is opposite a white.

Unfortunately that doesn't work here. You know I very much attempted to do it, but failed and decided I couldn't care enough to try to make it work.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

This kind of ruleset is fascinating for its use of "polarity". Even though two ends of strands are near each other, if both of them have just passed a truthful clue, they cannot link up, since then the liar clues aren't "every other" clue. In general, I think a ruleset that is "stateful" like this is worth exploring further.

The aesthetic theme of this puzzle is funny. The positions of the circles are symmetric along the main diagonal, but you probably don't really recognize this, because the top-left half has such a striking pattern that you might expect the bottom-right half to have something similar. Sadly that's not the case.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

There are a number of genres where it's so tempting to use only one kind of clues. There are a few Masyu puzzles out there with all clues being white. (There are also some with all black, but white is generally more flexible since it gives less information.)

Applying it to this variant makes it look pretty weird, though. It might look all white, but you know exactly half of them are black. (I could have presented this with all black circles and the puzzle wouldn't change a bit.) I also did my best to avoid straightforward deductions, like a circle on a corner being definitely black.

The result is a puzzle that might feel a bit unsettling. Overall it's still not too difficult, just gotta get used to the method of thinking with the Semi-Liar variant.

This puzzle was originally not mine. Zimodo wrote a Maxi Loop to serve as xi. (Had I written the puzzle, I would have looked into using X, I as Roman numerals, probably a puzzle heavily featuring the number 11.)

But the puzzle was very hard. IHNN, one of the top puzzlers in the world, was having serious trouble with it. I tested the puzzle and I had to do quite some bifurcation to break into the puzzle. We asked Zimodo, and that's also what he said: he got his feet dirty, dutifully checking all the cases to make sure there was no other possibility in the opening. Well, that's pretty bad. I like a hard puzzle when there's an actual logical path through it, but a lot of bifurcation feels quite awful.

In the end, I made the call to replace the puzzle. I kept the main ideas, including the theme, but made it easier and actually doable without too much bifurcation.

If you want to try the original version by Zimodo, look at the blog post.

Maximal Archipelago puzzles have an unsettling feeling. Sure, it only has shaded and unshaded cells, but in practice, I always mark whether an unshaded cell is "safe" or not. An unsafe one might still be turned shaded without breaking things, so I have to force it to become safe somehow. That definitely comes through in this puzzle, starting with a cycle of white cells already; you have to force all of them to become unsafe.

I also remember the first iteration of this puzzle was "disambiguate later". That is, I left open two potential paths that were symmetric, and only disambiguated which one it was at the very end of the solve. As explained in [2020-07-Typed-18] Starry Night, this is generally not a good idea. Maybe in theory it's fine — it's easy to just flip/rotate the grid, unlike other sorts of long bifurcations — but in practice, on paper you would need to erase the whole grid anyway (or work on a separate grid before copying the correct symmetry), and on digital you would need to clone the grid. I later changed the puzzle so the disambiguation came early.

This puzzle requires quite a tough global argument, one that I'm not even 100% confident on. I think this kind of argument also exists in Aquapelago and Guide Arrow, two genres I mentioned in my opening text. But I really like this puzzle, especially how it surprises you with absolutely no X whatsoever inside the grid.

I'm not sure how I came up with the idea of this variant. Back on my old blog, the rules page for this variant suggested I was trying to marry Minesweeper and Star Battle.

So why is it called "Sudoku" now? I feel the fact that the mines can be adjacent means it's closer to Sudoku than Star Battle. It does illuminate how similar Sudoku and Star Battle are, though. Sudoku (No Touch) is just nine 1-star Star Battle puzzles overlaid on each other.

This and the following two puzzles were actually posted on the same day, 26 April 2011. Given that most of my puzzle IDs are simply the posting date of the puzzle, that's a problem for this triplet. I could add something to differentiate them, like "a" to "c", but I decided I would just alter history and pretend these were posted on three consecutive days.

Also, it is a Sudoku if the regions don't all have the same size? Whatever, it's just a variant name.

Strictly speaking, the posting order on my old blog is not what you see here. The order was this 27 first, 28 second, 26 third. But I decided to sort them roughly by difficulty. I think 26 is the easiest, then this 27, then 28 is the hardest.

Want more Minesweeper variants? One of my favorite games is called 14 Minesweeper Variants. (It has a sequel too.)

Feels like there might have been some attempt of a symmetrical set of givens, before I gave up on it.

This was the first genre that I invented, although even so, I definitely got some inspiration from elsewhere. I think there was some influence from Str8ts, a similar puzzle genre that was commercialized. I got into a really dumb argument with its creator, something like my genre was not Str8ts but they insisted it to be called such (and said something about how Str8ts was "the perfect genre"), and that just put me off from the entire thing. That's likely a reason why I don't feel like writing Number in Order puzzles any more.

Also, I would (10+ years) later learned that Naoki Inaba came up with a nearly identical genre, called Straight Cross. I believe the only difference is Inaba's genre doesn't cap the number range. Everything is invented by Inaba, apparently.

This was very early in my puzzle journey, and I have barely started exploring themes. The black cells form "42" because I recognized it was a famous number, but the givens don't otherwise have any structure. The fact that it's unique is good enough.

Tilted square lattice is all nice and good, but I don't know why I decided to offset this pattern in a way so the pattern isn't symmetrical. I think it's intentional so that the solve feels different on the four edges of the grid. Although since it's the 2011 me, it's entirely possible I was simply still inexperienced.

This puzzle is pretty funny. You need to flip the "sided-ness" of the 2-3 pair, but one way is blocked with the 1 clue. For some truly beginners, this might have been enough of a challenge.

The solution leaves one empty space, but extending the 1 to use the empty space causes a second solution (well, a family of solutions) to pop up. Honestly that's pretty neat.

The original puzzle was not unique. Yes, it's part of a contest. For this archive, I modified it by moving a couple of clues to fill in unused cells. I've since learned I'm not comfortable setting Numberlink puzzles, mainly because it feels so hard to make it unique and it's usually solved through intuition and heuristics.

Did you know? This puzzle wasn't the original puzzle. The original puzzle had a 3 on R3C3. It was unique, but I decided to change it to a 4 to give it a stronger aesthetic theme: the clues are now 2 to 7, no repeats.

I discovered a theory in Nurikabe puzzles, and I wanted to show it off using a toy example. This is the puzzle I decided to write for that. It can be easily solved intuitively, but I believe you need the theory in order to prove the solution is unique.

The contest's whole idea was that each author would get to use their section in any way, generally to introduce themself. I was trying to figure out how I would introduce myself, and I decided on a few selections.

Nurikabe isn't my invention, but the gridpoint argument is. This puzzle does use the argument. It also features two of my favorite Pokémon: #492 Shaymin and #471 Glaceon.

This might be a vanilla puzzle, but oh boy the aesthetic is so great. Yes, it's evens and odds, but the rotationally symmetric odd clue is exactly 1 more than the corresponding even clue! Not just that, but the solve is also pretty; it is a slightly different flavor than your usual Nurikabe puzzles.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules. Although this one isn't too much of "another genre".

As far as variants go, this feels pretty tame. I don't think the puzzle is particularly notable, but that's okay, more standard puzzles are fine in a contest.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules. Although this one isn't too much of "another genre".

Aesthetically, this puzzle is pretty wild. There's a 43. The right column is 3-1-4-1; it might have been inspired by pi, but I think it's more a coincidence, since the 43 isn't related.

I think this puzzle is great, even if it's less of a Nurikabe puzzle and more of... some other genre. The logic is just so bizarre and delightful to figure out. Surprisingly little counting if you know where to look.

The reason this variant is included in the contest is to show off the gridpoint counting argument I developed (explained in [2019-05-19] above). But I think it's generally a tricky argument, so I reserved it only for the large puzzle. The small puzzle made use of the variant, but not the argument.

This puzzle makes extensive use of the gridpoint counting argument. If you don't realize the full implications, it's very easy to accidentally close off a possibility and get nowhere. I also tried constructing the puzzle to be resistant to intuited guesses, although I think it can never be fully ruled out.

I think this is known as a different variant name elsewhere, but I can't recall what it is. It's called "Lovers Nurikabe" in the contest, though, and is part of the Lust sin.

The execution here is definitely pretty interesting. Although the puzzle solves pretty easily after the break-in, I think I like what it's trying to do.

Honestly, this puzzle is quite embarrassing that I was considering skipping it, but it has an important story.

You might be wondering why there's this strange rule about no cycles. I didn't know either! My very first exposure to Nurikabe was from a book in which it introduced the rules as above. I was actually confused when I learned the actual rules of Nurikabe, and for a while I resisted the change (including making this puzzle that would be ambiguous by normal Nurikabe rules). Over time I learned better, though, and now I follow the usual rules of Nurikabe. This puzzle serves simply as a look back to my history getting into logic puzzles.

I don't remember what transpired me to make this theme. But it works!

I also don't remember what made me write a Pentominous puzzle. I mean, I think it was assigned to me, but I'm actually not very good at Pentominous. So it's surprising that I ended up with this tricky puzzle which was worth 75 points out of 550. That's a pretty significant chunk of the total.

Also, apparently the pzprxs URL has a ton of "hahaha"s. Just letting you know.

The following six puzzles were actually not posted independently, nor were they posted on the 1st to 6th of the month. They were posted together, as practice puzzles for NEW, HUGE, AND CHALLENGING!. The contest brought a new genre, and the actual puzzle [2016-03-NHC-1] was massive and ruthless, so I figured some practice would be useful.

A linear order simply gives standard Futoshiki, but I figured that's fine. It shows that this is a generalization of the standard genre, and it helps people get used to Futoshiki logic if they have never done any.

This puzzle has two separate chains that don't interact with each other. They are still distinguishable though, since one is longer than the other.

Poset Futoshiki can have some lateral thinking moments that aren't usually found in logic puzzles. Not that they are necessary, but they are usually helpful to frame your perspective.

For example, look at the poset here. Despite the unusual appearance, it's barely anything different from the total order: only two pairs of numbers are incomparable. Then the solve is somewhat similar to usual Futoshiki puzzles, except for these two pairs. A good puzzle will make use of these missing two pairs to drive a lot of the solution. Whether this puzzle is "good" by that definition or not, though, is something you'll have to find out.

This might look like a weird poset. It actually has a hidden rule: X < Y exactly if Y is a multiple of X. The example puzzle is also similarly a divisibility poset. This is another example of lateral thinking; if you don't get the structure of the poset, you can still solve the puzzle just as fine, but it's likely more difficult to think and visualize it.

In general, I like having no givens in the grid for (Poset) Futoshiki puzzles, which means the poset cannot have any nontrivial automorphism: you shouldn't be able to permute the numbers and get the exact same poset. For divisibility posets of N elements, the only values of N that have no nontrivial automorphisms are: 1, 2, 4, 6, 10. For instance, if N = 7, 8, or 9, you cannot distinguish 5 and 7. But for N = 6, there is no "7", while for N = 10, the number 5 now has an extra inequality 5 < 10. But for N = 11, now 7 and 11 are indistinguishable.

For that reason, I really like to use divisibility poset on 6 elements. 4 feels too small and 10 feels too big.

Strictly speaking, the numbers don't have to be 1 to N. They are just labels, I can use emojis if I really want to. (Sure, the rules for Poset Futoshiki above say to use 1 to N, but I can very much change it.) But it makes understanding the poset harder.

This poset has a bizarre, alien feeling. There are so few comparable pairs, and there isn't even any case of X < Y < Z. So a single inequality sign carries a lot of information.

You might recognize the entire puzzle is almost antisymmetric, except the column 1 and column 6 clues aren't reflected. I definitely don't want it to be fully antisymmetric, since the solution would be antisymmetric too otherwise, but it's a fun way to construct the puzzle.

This has some similarities with [2016-03-03] earlier, since there are few missing pairs. But when I wrote this puzzle, I didn't specifically look for that; I simply wrote down a poset that looked fancy, and made a puzzle based on that.

Ultimately though, these six puzzles are all just warm-up for the real behemoth, [2016-03-NHC-1] coming up. Good luck!

Since part of WAPC is showcasing who I am, of course I included one of my inventions. Poset Futoshiki is one of my proudest creations, even though it's just a variant of an existing type, because of how cursed things can get.

This puzzle shows one such case. My other two puzzles, the Nurikabe and the Fillomino, were pretty easy. (Okay, the Nurikabe is easy to intuit, not prove, but it still has a low score.) In contrast, this puzzle is one of the highest-scoring ones. It's difficult with a narrow path. It's purely logical, although the break-in might take a good while to find.

I like how the pattern of givens are basically reflected over the vertical axis, just offset by 1 cell. Otherwise, not an obvious puzzle to solve, but it has some general tricks of what you're expected to observe in Poset Futoshiki puzzles.

The fact that 3 > 4 > 5 caught some people off guard. I wonder if I should have used letters (e.g. A–G) instead of numbers, just so the natural ordering of numbers doesn't come into play.

After bringing Contact to more people, I decided to try making another genre that's interesting and simple. Then I remembered this math problem; see the text under Rampage above for more about this problem. So I was curious about turning it into a logic puzzle genre, and here we are.

Somewhere along the way, I definitely dropped the "simple" condition since the ruleset is pretty tricky to write about, although arguably it's still pretty intuitive. Not just that, the solve was absolutely not simple at all. The genre brings so many wonderful theorems to discover, but you kinda have to figure them out before you can reasonably solve puzzles in this genre. And I'm not yet sure about the depth of the genre after those fundamental theorems.

I haven't tried my hand in writing another Rampage puzzle; the complexity of the ruleset does make me nervous. But perhaps one day, and perhaps I'll also learn how to write Rampage puzzles with aesthetics.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

But maybe you want to look at the next puzzle [2015-01-Polyglot-57].

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

This one is special, though. This and the previous [2015-01-Polyglot-52] have the exact same grid, making it a "Schrödinger puzzle". I absolutely have a sweet spot for these, especially when the genres are contrasting. Nikolai Beluhov used to maintain a list of these. That said, they are very difficult to construct for obvious reasons.

Since this is part of a hunt puzzle, though, I'm not sure how many people appreciated it. Also, it has no aesthetic theme whatsoever. That's fine, due to the structure of the hunt puzzle; besides, making Schrödingers is a very hard job, and adding more constraints on top of that might be too much. But it would be pretty nice.

As explained in the Instruction Booklet, this genre was invented to capture the process of creating Polyglot, where I had to occasionally make a Schrödinger — the same grid being solvable under multiple rulesets. One of the Schrödinger pairs were [2015-01-Polyglot-52] and [2015-01-Polyglot-57] above. Now you get the experience of constructing the grid so that both rulesets have a solution.

This genre is pretty difficult by itself. You basically can't trust anything, since you have no idea whether a dashed circle is black or white, and that leads to entirely different conclusions on either grid. I think you need to do some bifurcations here. Mild bifurcations that break quickly, but still trying out cases anyway. Still though, there's some quirky elegance to the ruleset.

Linked Signals only has one clue type, so it's hard to do aesthetic themes. Although, the definition of the ruleset doesn't prohibit me putting black/white circles directly onto the grids, and they don't even have to line up. It just feels inelegant if I do so.

You would think a 5×5 puzzle wouldn't pose any problems. Well, you're wrong. This puzzle wasn't solved by anyone in the championship. And this is the small one!

It's probably possible to intuit into the solution, but the solution is pretty unusual-looking for a Simple Gako puzzle, so even that isn't straightforward. And while I can prove the solution is unique, note the word choice I used. "Prove". I had a fairly involved mathematical argument to show the solution must indeed look like so.

With the large puzzle, I decided Simple Gako was too difficult to put pretty patterns, so I opted with a very weak aesthetic theme. The givens come in diagonal pairs. If you realize that you can permute the rows and columns of a Simple Gako puzzle, you'll realize this is a very weak theme. I focused entirely on the logic here.

In a way, I think this puzzle is more straightforward than [2025-05-Serbia-11] above, in the sense that intuition can likely carry you better. The part I'm struggling was with the uniqueness proof. I think I have a proof, but I'm not 100% confident. That's how cursed Simple Gako puzzles are to solve and write.

Some people think Skyscrapers puzzles shouldn't have given numbers inside the grid. (I believe the pzpr implementation didn't even allow inside givens in the past, although apparently now it does allow them.) It's definitely cleaner to have no given numbers, but sometimes I think the trade-off is worth it.

In this case, the 1s inside the grid are symmetrical and equal, so I feel they are still quite pretty. I did try to find several alternatives, but nothing came out nice, and I decided this was acceptable.

I really like the logic; the variant rule has some surprising implications. It's one of the harder puzzles in the set, but I think it's logical and clean, and it's rewarding to solve it.

According to the Solution Booklet, I constructed this puzzle with computer assistance, probably in a similar way as [2020-07-Typed-18] Starry Night. There aren't that many solution grids, so I threw in various clue patterns that looked cute, and if there was a unique solution, I tried solving it by hand to check if the logic was acceptable and interesting.

That said, I'm not sure why I had inside givens. Both this and the large puzzle [2020-11-25Y-16] had the "25" pattern (representing my age of course), although this one as inside givens while the large had outside givens. So I might have constructed the large puzzle first, and decided to put the "25" as inside givens for this small puzzle. Otherwise I certainly wouldn't have thought of putting inside givens for a 5×5.

So, was the logic acceptable? For sure. I think this one is a pleasant solve. It doesn't use the variant rules too much, but it does at a couple key moments, and it can serve as some sort of tutorial to prepare you for the large puzzle.

Brutal. There were four puzzles worth 200 points (out of 2525), but I think this one is the hardest of those four. There exists a logical solution path, but it's very narrow and very long. In a way, it resembles [2018-05-24HPC-27], the puzzle that inspired me to put this in the contest in the first place. I think it's incredibly worthwhile to solve, though, with virtually no lookahead.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules.

I love involving outside clues as if they were cells of the grid, and Skyscrapers is a huge breeding ground for those kinds of variants. In addition, like Masyu, there are only two types of clues in Kropki, meaning an antisymmetric layout is often a striking aesthetic theme.

That's exactly what I did here. The puzzle isn't too difficult — although it has some tricks — but the theme is great.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules.

In [2013-05-Deception-17] above, I mentioned genres with two kinds of clues can try to do an antisymmetric pattern. Another way to execute a striking aesthetic theme is to use only one kind of clues.

That said, that wasn't entirely how this puzzle started. I believe it was initially "many clues on the outside", and I found out a lot of them could be white circles, so "all white circles" became a second theme.

Now, you might notice almost all of the outside ring is almost entirely white circles, but not all. It suggests the ones that don't have them are not consecutive, otherwise I would have put more circles there. Is it true? You'll have to find out. But still, I think I could have given a pattern on the outside, so that the absence of white circles can be more meaningfully attributed to the aesthetic theme, rather than because the circle doesn't fit there (or that I'm trying to trick you).

How does it solve logically? Oh boy. It's hard. The solve path is narrow. But it's there. Good luck!

I don't remember the exact circumstances that led to this puzzle, but it likely involved Jamie Hargrove. Jamie likes his liar puzzles, and I thought about whether it made sense for a Skyscrapers puzzle. Turns out it could make sense, and it's a pretty silly theme, too: all the clues are staring at this one lone guy at the top side, which is clearly lying.

This is the first puzzle I've ever published online. I don't remember if I've written any before this, but what are puzzles if not meant to be shared? I believe I published a few puzzles at once, not just this one, but this was puzzle number 1 on my first blog.

Clearly Slitherlink was my favorite genre during my early days.

The blog post that had this puzzle said that I was "in a happy mood today; how did you know that?" Safe to say my jokes were corny. (They still are.)

The first time I posted this puzzle on my first blog, it had no solution (I think I transcribed something wrong). But I published it to my second blog too, and I definitely recognized the issue then because I made a stealth change to fix it.

I think this might be my first 10×10 puzzle? It's the first Slitherlink one, at least. Also, I'm amused that I called this puzzle "difficult" back then; it's now easy-to-moderate by modern standards.

I'm lying, this wasn't made in 2011. This was made in 2023, specifically 25 January 2023.

As I described in [2011-03-18] above, originally it had no solution when I first posted it on my first blog, but I recognized the issue and fixed it for my second blog. This puzzle also originally had no solution and I also fixed it for my second blog… except the fix was also broken. So I fixed it up again for this archive, meaning this is technically a different puzzle from either of the two. Hence why it's made in 2023. (As an aside, on my second blog it was posted as "a beginner would be able to practice with this puzzle". ha ha not if it's not unique)

Yeah no the pattern is so sad. I don't know why I made this pattern.

For a 2011 puzzle, this has quite a pretty aesthetic with the large empty middle.

In BMPC, this puzzle would only be given "once the participant has scored 150 points" (out of 250). Because 10×10 is obviously large and menacing. It's still relatively easy for modern standards; it's mostly overclued.

On my blog, I remarked that this puzzle had "a 31% density of givens" and was thus "quite a difficult thing to solve". Over a decade later, I'd be inclined to agree with Robert Vollmert's comment, "it is not difficult at all". Shows how I've grown over the years.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

Quite a number of liar variants rely on "exactly one clue is lying in each row/column". Why don't I make your job as hard as possible and give all the clues, so it's the maximum possible confusion in what clues are lying?

On one hand, this puzzle becomes pretty tedious. You have to scan the grid to figure out where the break-in is; there's no clue from the pattern of what cells have givens, since all cells have givens. On the other hand, I do think it's pretty cute. I think "2" is the least informative Slitherlink clue, so spamming the entire grid with it does work. The logic is pretty nice, and I think I like the idea.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

I think I really like the idea of the break-in for this puzzle. It's something that feels uniquely due to the liar variant. I think the execution could have been a bit better — the puzzle feels a bit too symmetrical — but it's still really interesting.

I find it fascinating when Slitherlink variants basically want you to shade cells to be inside or outside the loop. It's a different way to look at the genre, and often it leads to interesting deductions. This puzzle, while small, uses quite a wide variety of techniques; for a puzzle written during my early days, I'm still rather proud of this puzzle.

When I first put this in the archive, I remarked Penpa didn't have sheep and wolves, so I used shapes: white diamond for sheep, black diamond for wolf. This was inspired by the coloring for Castle Wall. (The presentation on my old blog was similar, but the colors were reversed, and the diamonds there were Unicode symbols.)

Later on, I replaced these with sheep and wolf emojis, which were cute.

Even later on, I found out Penpa changed its font to render emojis, and sheep and wolf now looked awfully similar. So I had to re-introduce white/black too to distinguish them, this time with circles.

Why am I trying to avoid using "S" and "W" so hard? I guess I just want to be cute.

This puzzle barely uses the variant, which I also recognized back then. I would even say the variant was a "patch", a rule that was added mostly just to resolve a small uniqueness issue at the end. Noawadays, I would use the variant much more, something like Serkan's puzzle in 2021.

Back then, the variant rule was called "Star Battle". For some reason, I didn't include the rule about non-touching stars, so I'm changing the variant name for this archive. I would even change it further by using objects other than stars, but I couldn't find any good one.

In the original version of the puzzle, I introduced a new element that simply marked a cell couldn't have a star. When I was porting it here, I realized it simply meant the clue was a question mark: you don't know what number goes there, but you know it's not a star.

This variant was invented by me a long time ago, but I hid the shapes. Later on, Nikolai Beluhov tried constructing one, and like all Nikolai's puzzles, it's so pretty to see and so intimidating to solve. In particular, though, it showed all the boundaries, and I liked it enough to adopt it.

A similar genre also appeared on Grandmaster Puzzles, Slitherlink (Sudoku) by Carl Worth, with the additional constraint that each row/column contains each number once (among the hidden cells). I think it can be neat, but ultimately might be too restrictive. The shapes alone already give some logic, the row/column restriction is not further necessary.

When the clues are hidden, it's very easy to make ridiculously difficult puzzles, so for this first puzzle, I gave one visible number in each shape. That helps making it more approachable.

Theory-based puzzles are always fun. Those are puzzles that require some sort of theorem to be proven separately, and then the puzzles themselves are an application of the theorem. Gridpoint counting in Nurikabe ([2019-05-19] Nurikabe) and penalty theory in Heyawake ([2020-05-09] Heyawake) are examples of them.

This one turns out to require a small, perhaps pretty specialized theorem for Slitherlink (Tetromino) puzzles. The 2×2 square shape is repeated many times, but in such shape, the 0 and 3 are in close proximity with each other. Surely there aren't many ways this can happen.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

This genre was invented by Zotmeister. I believe this is where the term "dynasty" comes from. The "Smullyan"-ic part comes from Raymond Smullyan, who wrote a lot of puzzles involving knights (which tell the truth) and knaves (which lie), tasking the solver to figure out who's what. This genre was invented in 2005 (!) and it was under-explored back then, so I decided to take this into the test. (It is still under-explored now, although there are several more puzzles out there.)

Every cell is clued. Not only that, the clues are all 1 and 2, pretty uninformative ones. What can you do?

Turns out the puzzle is still fairly easy. Once you figure out any one black cell — "knave" as per Zotmeister's wording — you basically solve the entire puzzle because fully-clued Minesweeper is pretty easy. I also found it difficult to figure out what kind of logic I wanted. And similar to [2013-05-Deception-01] Slitherlink (Liar) in the contest, a fully-clued grid obscures your intent, in a way that's not very fun. It's easy to have alternative break-ins, and I think I went into the puzzle without any particular remarkable logical step.

For a puzzle I wrote early in my puzzling journey, it's pretty good. Nowadays I might try to tweak things and see if I can get something better, by e.g. emphasizing the logical step better. The theme can be immensely rewarding if I can nail it; I just need to complement it with nice logic.

Deception is divided into three sections. This puzzle is in the first section, "Falsehood", with clues that lie in a way or another.

I feel like I didn't find anything particularly notable from this puzzle, other than its aesthetic theme is nice. But for a contest puzzle, a quiet, chill puzzle isn't a bad one.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

It's impressive how few clues a Square Jam puzzle needs to make it unique.

This also serves as the easiest puzzle in the set. True, with completely novel genres, even a simple puzzle might prove a challenge since you're not familiar with it. But this hit the mark, getting the most solves out of all the puzzles.

Square Jam also feels flexible. It's true that a few clues are enough to make a puzzle unique, but you also generally have free reign on where you can place the clue. That means it's pretty easy to design puzzles with certain aesthetic themes. Here are two rings, in a puzzle genre about squares.

A few days before this puzzle, there was a discussion in Puzzlers Club about 9×9 Regionless Star Battle puzzles. 9×9 is a tight grid (with 2 stars), so you often only need to rule out a few cells to force the rest of the grid to resolve. It leads to visually striking puzzles, where at first they look impenetrable, but they still end up having a unique solution and resolving very nicely anyway.

I decided to try my hand on it, and this is the puzzle I wrote. The theme is "the grid is torn". I'm sad I need an extra empty cell at the top-right, but I'm still very happy with this puzzle, especially since I think it's has a pretty unusual solve path for a Star Battle.

Hint

A basic deduction in Star Battle is that a 2×2 block can only have at most one star. Consider rows 1–2. We can fit in three 2×2 blocks on the right (marked with circles), so they collectively have at most 3 stars. The remaining 2 cells, R1C3 and R2C1 (joined with green line, the upper one) must then have at least 1 star. We can do the same deduction in columns 2–3, so R1C3 and R3C2 (lower green line) must have at least 1 star too.

Now, these two pairs of cells overlap at one cell (R1C3), and the other cells of the pairs (R2C1 and R3C2) are adjacent. If the overlap was empty, the other cells would have a star each, but then two stars are adjacent. So the overlap must have a star, as indicated.

You can do the same deduction elsewhere, and these two stars will lead the solve.

For some reason, I thought of more 9×9 Star Battle Regionless puzzles. I had an idea that I could place a 3×3 hole on the grid and that would break all symmetry. The hole isn't quite 3×3, but it's close.

Sometimes I wonder whether puzzles are invented or discovered. In many cases, they are invented, but sometimes the stars align (get it?) and something ends up unique by seemingly pure coincidence. I think this puzzle is an example of that latter case. This hole position is the only one that's internal (not touching the border) and breaks all symmetry of the grid. There are only two ways to orient this particular hole shape. (The other orientation led to two solutions, by the way.) And just like that, the puzzle's unique without needing to do anything else, and the solve is pretty nice. It felt like pure chance.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

I actually posted three Sudoku puzzles on this day, because a (high school) friend asked me to write some puzzles. But they were rife with issues: the first one had no solution, the second one had three solutions, and the third one had an off-symmetry clue. I promised to get around to fix them, but never did.

Well, until now, to some extent. This is the first puzzle, but now fixed to actually have a (unique) solution. I only had to change one cell, so it's likely a wrong transcription. But because I've entirely forgotten how my original puzzle worked, even a one-cell fix like that took a long time; I had to solve as much as I could, I had to try to ignore different combinations of cells to figure out where I might have made a mistake, and so on.

For that reason, I'll only fix this one puzzle, at least for the time being. (And even the reason I fixed this one was just to have space to tell this story.) The other two are low priority, if I ever get around to them at all. You can look at them though: three solutions and off-symmetric clue. Feel free to try and see if you can repair them.

As a side note, the smiley face pattern of givens is identical to [2011-03-10] Slitherlink a few months ago.

Very straightforward puzzle, but the more important thing is that it's valid, and it has a pretty decent theme. (The main diagonal spells the value of pi, and there are two shapes of pi in the other corners.)

Wow, I wrote so many Irregular Sudoku puzzles for BM Puzzle Competitions. Mainly because the target audience was pretty new and barely familiar of anything else, so I stayed with known and easy stuff. These are basically fillers, so I'll just present the rest without comment.

This and [2011-05-BMPC2-2] below were a pain to typeset. Hope you can live with this.

There are many mathematical variants (on Sudokus and other puzzle genres). But I think equations are overly general. It's pretty easy to make a huge mess with the equations and make things hard to read, like in this puzzle. I think even TomTom is a bit pushing it. Arithmetic-based variants want a more restricted form; for example, Sudoku XV (pairs of adjacent numbers that add to 5 or 10 are marked) is cleaner.

The one saving grace of this variant (see [2011-05-BMPC2-1] above) is that it can be used to produce beautiful puzzles. I think this one has an excellent theme, and it's perhaps worth setting up the variant to present this puzzle. If I were to redo the competition, I would keep this and replace the previous one with a better puzzle.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

Elimination is a pretty common variation of Tapa. It's not common to have a puzzle genre that fits this style: digits in a clue represent different segments, so that it makes sense to add digits and ask you to remove one.

Likewise, Elimination allows for an interesting theme of making many clues look similar, as I did on this puzzle. I think I went with it a tad too far, though; the puzzle became pretty easy logically, possibly way too easy.

This is a lesson I would learn over and over again: aesthetic themes are nice, but they shouldn't get in the way of logical themes.

Deception is divided into three sections. This puzzle is in the second section, "Ambiguity", with clues that don't tell much.

One aesthetic theme that often catches my attention is "almost symmetric". The whole puzzle is almost fully symmetric, givens and all, except for a difference. This puzzle shows one: only the clues on R2C3 and R9C8 are different, everything else are equal with its rotationally symmetric pair. Of course, such puzzles are the best if the solution is as non-symmetric as possible.

Overall, I think I like the theme and the logic of this puzzle; also note how all digits are 1's and 2's. There's only one blemish, though: the two "? ?" clues. I think I just needed those cells to be empty. I should have tweaked the puzzle better to not have those cells, but I think I'm still pretty happy with the puzzle, especially for something I wrote in 2013.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

Abacus variant is particularly strong for Tile Paint, as it appears. That said, I'm not sure the puzzle is very fun; it's kind of bifurcation-heavy. But maybe I missed some more logical way!

I mostly chose the genres to have the TGE initials. I'm not sure why I didn't chose Tapa, though.

(The image is still PNG because Penpa has some bugs when exporting arcs into SVG.)

More Tile Paint, more... bifurcation? Well, the Wall variant helps, but the pattern of the regions is exceptionally awful for walls.

In the Greek round, every puzzle is themed after a Greek letter. The theme is meant to appear in the puzzle itself; it's not necessary for the theme to appear in the genre. Eta, though, isn't really used much anywhere, so I had to look deeper, probably away from the Greek letter itself. I then realized that E, T, A are three of the most common English letters. One fun peculiarity is that ATE, EAT, TEA are all common English words. ETA itself is a word, obviously. What genre could make use of it?

Three-letter words, each letter has three possibilities. I remembered a genre by Palmer Mebane: Triplets. In the original, it had 3-digit numbers made of the digits 1, 2, 3, but there's no reason the symbols had to be those. I adapted it to use the symbols A, E, T. Then I could give ATE, EAT, TEA, and of course ETA itself as givens in the puzzle. I also realized TEE was also a common English word, and having five givens really helped.

The genre itself was... "cursed", in a way. I tried constructing a puzzle, and it was frightening how the possibility space initially looked really open, only to suddenly close shut into zero solutions. I think this might be true for genres where you have to place each thing once on the entire grid in general, because it means things you put on the grid can affect very distant places.

I ended up with a really difficult puzzle that required a lot of some high-level analysis, but I'm immensely proud of the puzzle and fought to keep it in. The grid also managed to be shaped like an eta (η).

In December 2023, I was thinking up of new genres. At this time, I had started to publicize Contact, and invented Rampage just a few days ago. Both of them were region division puzzles, so I tried thinking of other things. I came up with the idea of loops. Personally, I find the rules for loops a bit inelegant; it takes some time to explain the loop can only travel orthogonally, cannot cross, and so on. (Although it's easier than explaining the rules for a wall like Nurikabe and Tapa.) So I looked for something particularly simple to complement this.

I then thought of Masyu, and how its clues depended on turns on the cell with the clue, as well as cells immediately before and after it. What if I made a different clue type for it? Counting turns was the most straightforward, and the genre came out that way.

The genre seems to have a lot of freedom. (Contact and Rampage tend to wow people by how few clues are being used, but that does mean it's pretty hard to set puzzles, given a clue has far-reaching effects.) For this puzzle, I went for a theme of today's date, in addition to my usual schtick of symmetric clue placements.

I suspect Turnaround has similarities with Masyu, in that there are patterns you can learn. This puzzle focuses entirely on the number 2, and you'll pick up a few patterns made of 2's that exist in this genre.

There are lots of patterns you'll have to figure out and apply here.

I forgot how I wrote this puzzle, and when I solved it again, I ended up having to bifurcate near the end. That's a blemish, but for this beautiful aesthetic theme and solid logic elsewhere, I think it's acceptable.

Variant rules: Turnaround rules. In addition, there are abacus circles (thermometer shapes forming loops) on the grid. Every time the loop visits an abacus circle, note the number of cells visited contiguously along the abacus circle before the loop leaves it. All abacus circles must read the same way, starting from somewhere on the circle and reading in one of the two directions.

Click for an example

The following example shows a loop on two abacus circles. Each abacus circle reads 1-2-2-3 (the left one clockwise, the right one counterclockwise). Note that what matters is the order along the abacus circles, not the order along the loop.

Puzzlers Club has a series of events called "Logic Showcase", where people are invited to write a logic puzzle based on a particular prompt, then the puzzles are published and people vote for their favorites.

I have just run Logic Showcase 61, where the prompt was "a genre I invented". I received quite a lot of entries and compiled them on a special webpage. But I didn't want to miss out on the fun; I decided to also write one entry myself and presented it along with the others.

This is that entry. It combines Turnaround, a genre I invented (which I think has great potential), with the Abacus variant, a variant I implemented after an idea from TheGreatEscaper. Be warned, I think it's very tough.

In theory, I really like the concept here: a puzzle that seems fully symmetrical, except the center of rotation is not the center of the grid.

In practice, the solves for the two halves aren't sufficiently varied. Symmetrical designs are fun, but only if the solve is not symmetrical. Otherwise, you only have half a puzzle.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules.

This is probably the dumbest puzzle in the contest. Spoiler, it uses the "rotate but no reflect" rule. But only to disambiguate something at the end. When it was presented in the test, the ships were packed more tightly, and that 1-ship looked like it was part of the S-shaped ship. There was a solution with that assumption, and someone complained about it.

Even thematically it's a mess. First, the fact that I needed a 1-ship was bad, I should have tried to ditch that. Second, I'm "chaotic", or "chao" at best; I should have dropped the S too. And perhaps more minor, but the O probably wanted to be a 3×3 donut.

I think this is the weakest puzzle of the set, and I should have cut it. But my 2013 self was still learning things.

Deception is divided into three sections. This puzzle is in the third section, "Annexation", where each genre takes up another genre to modify the rules.

This puzzle is a much better execution of this genre, compared to [2013-05-Deception-13] above. At the very least, there's no trap of "rotate but no reflect" with this standard fleet.

There's an 0-up clue on the top row. That tells me, this puzzle was written before I embraced gray cells in Yajilin. (It might even have been before this became commonplace in the puzzle community in general.) Originally I removed it to try to clean it up, but I decided it's better to present it as is so I can also explain the story. But I can't help but think, given that we now have gray cells in Yajilin, whether this puzzle would look different if I only kept the 0–5 on the top-left there, and only used empty clue cells to construct the rest of the puzzle.

Anyway, the puzzle itself is quite tricky. There's a deduction involving dense Battleships rows that I haven't quite fully fleshed out even now, other than mostly trying things out and seeing whether they may lead to a solution. It's worthwhile to try, though.

I originally invented this variant for a puzzle contest named "EVIL", which had novel variants. But the test didn't happen; I didn't manage to follow it through. (I do still have some files about it; I'll see about publishing them here.)

Considering the name of the test, this variant is relatively tame. The short condition does force some unusual deductions, though.

Also, yes, the "Yajilin" part is axed here with all the clues, it's just a Simple Loop. I even called it out in the Puzzle Booklet. I think Simple Loop with this variant might already be interesting enough.

As I explained in the Solution Booklet, I gave up constructing this Yajilin with symmetric givens. I decided to just stick with a very simple (and weak) theme of three 1s and three 2s. On the other hand, I could give it all the logical polish I could. This is a delight to solve, with some deductions you don't usually see in Yajilin.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

Since part of the "hindsight" round is revisiting past genres, this is one of them. The genre originally appeared in 17th 24HPC Round 3, written by Yunus Emre Büyükkale & Serkan Yürekli.

Honestly, this is a pretty fun variant. This might be influenced by the puzzle, which was kind of tough with a crucial step in the middle, but it's a satisfying solve.

Apparently I wrote this out of nowhere. I wanted to stream some construction process to Puzzlers Club, and I chose to do Yajisan-Kazusan. I've barely written or solved any, so this was also a new experience for me. It's not too weird, but I like the theme.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

We were having trouble figuring out something for Wrath sin, I'm pretty sure, because this doesn't seem like a very wise genre.

I looked at Erich Friedman's Puzzle Palace some time ago and was impressed by the wealth of puzzles. (I later learned that those puzzles generally aren't very logical, but it's still quite an impressive output with unusual genres.) I'm sure I remembered this genre at the time, and realized that it was very wrath-like: you're charging straight, as if mad and angry, only stopping when you really can't go further. So I set one and gave it the genre name "Rampage".

I'm not sure why there's a difference from Erich's ruleset, though. Admittedly, I actually think it's for the better; you know you really, really can't go past your own path, even if it's diagonal, which helps sectioning off parts of the grid. But also, I was having trouble proving the puzzle was unique, so I'm not sure I want to try writing more.

Update: I put this puzzle up on this archive, like, in February 2024. I only realized the Penpa is broken (it showed a different puzzle) now, August 2025. And I only noticed this because I had a file with my Penpa edit links and realized this one was missing, when I was doing a full update through all the puzzles. Nobody told me in the 1.5 years, geez.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

Hakoiri? What the heck is this genre even? I have absolutely no memory of why I made this puzzle specifically. Did I just look through genres on pzprxs (well, Puzzlink at that time) and choose one that caught my attention? Did I see something on Puzzlers Club that inspired me to write this? I have no idea. (Quickly searching PC, this puzzle is actually the first mention of Hakoiri at all.) Not just that, I think the puzzle itself is highly unusual for the genre, requiring unusual global deductions.

Well, it's here. I might not have remembered how I got this idea, but I think the puzzle is very nice to solve. Previous experience with Hakoiri might not help.

Since part of the "hindsight" round is revisiting past genres, this is one of them. The genre originally appeared in 19th 24HPC Round 5, written by Matúš Demiger.

The original genre was actually a variation of Slitherlink (and named "Fences Kropki"), allowing for Slitherlink clues in addition to Kropki clues. I figured the Slitherlink clues weren't necessary. Since this puzzle doesn't have any Slitherlink clues remaining, I think it's unreasonable to call it a Slitherlink variant, so I just replace the name for this archive. There might have been another name for this genre; I couldn't remember.

That said, not using Slitherlink clues made this genre really hard, and this was one of the hardest puzzles in the round. The theme is striking: it's completely symmetrical except for a pair of swapped circles, and the solution completely diverges with no resemblance between the two halves. But the difficulty is certainly through the roof. That said, our set had plenty of puzzles at lower difficulties too, so a couple at this level were fine.

Letter Weights puzzles tend to have clues that are meaningful words. I'm guessing I found it unfair for people that don't speak English — even though using English alphabet already gives that advantage in the first place, and the fact that this is an Indian Puzzle Championship where people usually have some English knowledge already — so I decided to have clues that sound like English, but aren't actual words.

I also like the fact that the puzzle only has 3 clues for 6 letters; that's unusually low.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

...I do have a comment about the genre, though. What? How did I end up picking this genre instead of something like Binairo? I think this genre is not particularly deep.

In the Zodiac round, every puzzle is themed after either one of the animals in the Chinese/Eastern zodiac, or one of the constellations in the astrological/western zodiac. We were having trouble figuring out what would fit "Ox". It's just not an animal that naturally appears in puzzles. The name is fun, though: it's made of two letters, O and X, resembling a circle and a cross. Those are some common symbols in logic puzzles. Maybe we could theme the genre after something using O and X.

Whenever you're not sure what genre to write for, always look at Naoki Inaba. There's just an insane output, of both puzzles and the variety of genres. It's a good inspiration for some incredibly obscure genres that might be under-explored.

I skimmed through all the various genres. (Someone on Puzzlers Club kindly compiled a PDF full of Inaba's puzzles; it's much easier looking through the book instead of navigating the Japanese website.) One genre that caught my attention was リメイズ, which seems to be transliterated as "Remaze". Not only it has O and X clues, but it's themed after a maze. I recall the tale of Minotaur, very closely related to mazes. And the Minotaur is a bull. Well, a bull is not an ox, but sure looks pretty close that I decided to call it so. I decided the genre was a perfect fit.

Then I tried to write a puzzle. I was having some trouble getting deductions. I went back to the puzzles on the page and tried a couple of them. I had all sorts of ambiguities. What?

Turns out, when I machine-translated the rules (with both Google Translate and DeepL), I missed the key rule about an O only having one branch to X. Some of my O's led to two X's (and some others not to any X at all). Well, of course I was having ambiguities. After someone pointed out that rule to me, I was able to solve the puzzles, so I went back to write a puzzle.

A lot of the puzzle was actually based on deductions I got before the key rule; for example, I realized a deduction based on parity that didn't rely on that rule. I kept most of it in the puzzle, although I added various parts based on the rule that helped drive the puzzle better.

Although this is part of a hunt puzzle, the individual logic puzzles were mostly constructed independently. That said, there may be some spoilers for the hunt puzzle, so my comments are hidden in a spoiler block.

Did you know Penpa can't check for suns and moons? Now I know. The choice of symbols for this genre is pretty neat, though, and I'm hesitant to change them. Maybe star and two colors of circles?

I ended up writing a lot about this puzzle, so I'm collapsing it to save space.

This puzzle is part of a hunt puzzle, Polyglot. It's intricately interlinked with the structure of the hunt puzzle as a whole, so I don't really have comments for individual puzzles.

...I do have a comment on the genre, though. I have no idea where I got the idea of this genre. It feels that the genre isn't particularly deep, although whether it's simply because this puzzle is not representative of it, no idea.

I didn't know this genre was not supported on Puzzlink until today; it sounded like a "classic" genre that Puzzlink would have. And this is also not the kind of genre I would normally even think about, so I have no idea why I ended up writing this puzzle. I'm guessing we brainstormed several ideas, including genres that were related to the digit 3, for anyone to pick up and write a puzzle for.