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. (The 10x10 Slitherlink is likely my second.)

Themeless, pretty straightforward. However, I think this was my first ever Cave and I was feeling out the genre.

The theme is nice and the solve path is fun, but I don't remember why I wrote this. Maybe I was just feeling like it.

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.

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 10x10 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.

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 a nice snack for experienced solvers and a reasonably filling meal for newer ones.

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.

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.

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.)

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 more obscure ones.

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 integral of 1/x can be bounded above using the harmonic series, 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.

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.

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.

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 easier to state, and it gets to actually have adjacent black cells for the abacus.

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.

Strictly speaking, this genre wasn't my invention. This being part of the Envy set in the contest, Joseph Howard was the one pitching the idea "the grass is always greener on the other side". We ended up at the idea that a neighboring region always has something you don't have, leading to this ruleset.

I don't remember why Joseph didn't write a puzzle for it, though. One possible theory is that he might have had, but we decided the puzzle wasn't good for one reason or another, and I took up the job to replace it.

Either way, the genre became associated with me, especially after I ended up using it in 25 Years. I'll call this genre my invention all right.

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

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 25 Years, 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.

In the Puzzlers Club server, there are events known as Logic Showcase, where people design logic puzzles to a given prompt, and then people vote for their favorite. One of the showcases was to write a Haisu puzzle, so I wrote this one.

I intentionally kept it pretty simple; I knew Haisu was a mind-boggling genre and it was very easy to end up with something very difficult. Even so, this puzzle is far from trivial. It takes some work, although I believe there shouldn't be excessive lookahead.

One fun thing about Haisu is that there are two sources of asymmetry. The fact that the path is directed means S and G behave differently. Moreover, two regions that are symmetric might not only be visited differently, but a different number of times too; a 2 might be something early (if the region ends up being visited 3 or 4 times) or something late (if it ends up being visited 2 times). It's really fascinating, and I found myself setting a puzzle that was completely symmetrical (except for S and G), and yet resolved completely differently.

I ended up winning the showcase with this entry. I believe part of it was due to my simplicity and aesthetic theme. Many other submissions were much more difficult, and I think some of them went overboard: there was an entry that was 29x29 and had a "107" on the grid. In a way, my puzzle is among the easiest of the bunch, and so perhaps the most solved by people casting their votes. (What good is a puzzle that's pretty if you can't solve it to verify that?)

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 one of my Haisu puzzles, this was also an entry for 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.

Initially, I only contributed the Fillomino. I tested the other puzzles that lovemathboy wrote, though, and we decided one of them (a Slitherlink) wasn't fun or cursed enough. I also noticed we were lacking in region division puzzles, so I wrote another.

When I tested this puzzle to add to my archive, surprisingly it's also pretty cursed; I was staring at a half-filled grid for a good half an hour or so. I think it might just be because I didn't quite recognize the implications of the ruleset.

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: Penalty theory in dynasty puzzles (by tckmn) and Teal's Mini Heyawake Guide :)) (by Teal).

Some time before this, I had also come up with a kind of penalty theory for Nurikabe (although it's less used). In addition, there was also something called river theory for Heyawake. The common thread to all of these is that they are all based on deep mathematical theory embedded in logic puzzles; nowadays, there are several enthusiasts for these kinds of puzzles, with some authors writing about them.

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.

You might also notice that this puzzle is pretty recent! I don't know what came to me. I just felt like wanting to write something.

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.

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 is an incredibly unfortunate aesthetic theme. The theme was almost there! Not only a bunch of increasing sequences, but the left ones increase by one going up: 3-4-5, then 4-5-6, then 5-6-7. And what happens with the right one? There's 6-7-8 and 7-8-9, but the bottom sequence is also 6-7-8, not 5-6-7. Awful. I'm sure I tried so hard to make 5-6-7 work, but that failed.

I learned from an excellent article by Mark Rosewater, one of the game designers I most look up to, that "aesthetics matter". This puzzle has a good aesthetic pattern already — the multiple increasing sequences of three clues — but it was so, so close to having an even greater pattern, and that one thing broke the pattern and stuck out as a sore thumb. Either I would try to make it work more, or conversely, I would try to ruin the pattern so that it would only be increasing sequences, with no secondary pattern.

Anyway. The aesthetic issue is truly unfortunate. The puzzle is still good, though; it has a nice solve path, smooth and pleasant.

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. Since I couldn't be bothered to figure out a way to break the tie, I just labeled them with different dates.

Strictly speaking, on my old blog, the order of posting was: this one first, then the next one, then the previous one. But the difficulty was all over the place. I would call the previous one to be the easiest and the next one to be the hardest, so that's how I'm sorting these three puzzles.

Want more Minesweeper variants? One of my favorite games is called 14 Minesweeper Variants.

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

This is the first genre that I could say I invented. That said, I might have been inspired from Str8ts, a similar puzzle genre that was commercialized. In fact, I went into a really dumb argument with its author, and now I hate Str8ts and also dislike this genre myself.

I later learned Naoki Inaba came up with a nearly identical genre. I swear Inaba comes up with all the genres ever.

Either way, at this point I still haven't learned how to explore a new genre, but there are some neat little tricks. I also thought a theme of 42 would be funny because it's the famous number.

I have no idea why this pattern of black cells was not offset correctly to make a symmetrical pattern. I would say it was probably intentional so that the solve feels different on the four edges of the grid. But also, it was equally likely it was simply because I was still new and inexperienced in puzzle-setting.

I have absolutely no idea why I even thought of making this puzzle. Perhaps it's just to show off that I could have an unused cell?

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.

This puzzle originally had a 3 on R3C3. It was unique, but I realized I could change it into a 4 to give it a stronger aesthetic theme.

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.

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 all 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.

The six puzzles starting from this one are actually part of the same set: they were all given as practice puzzles for NEW, HUGE, AND CHALLENGING!. The contest brought a new genre, and the puzzle was massive and ruthless, so I figured some practice would be useful.

With a poset that is completely linear like this, the puzzle devolves into standard Futoshiki. Not that it's a bad thing; Futoshiki can also be fun by itself, and easing people with a "familiar" type isn't a bad idea. Wacky posets do lead to more fun, though.

The more incomparable pairs there are, the more strange the puzzle feels.

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.

I personally like having absolutely no givens on the grid, which means the poset cannot have any automorphism. There must be no symmetry whatsoever, because I can't distinguish them without givens. Among the divisibility posets, this is true for 1, 2, 4, 6, 10 elements only. For example, for sizes of 7, 8, 9 elements, you cannot distinguish 5 from 7. (For 6 elements, there is no "7". For 10 elements, 5 is no longer a maximal element because 5 < 10 while 7 is not < anything.) For that reason, I tend to gravitate to Poset Futoshiki of size 6 so I can use this divisibility poset; 4 is too small and 10 is too large.

Strictly speaking, the exact numbers aren't important and I can use a different set if I want. But then it's hard to remember which numbers are being used, just like it's hard to visualize the poset, so I just don't bother.

This poset feels so bizarre. I guess it's because it has so few comparable pairs, that any inequality sign carries a lot of information. That makes the puzzle feel quite unusual and unique.

It's fun to showcase different posets with different properties. But ultimately, these six puzzles are to prepare you for the behemoth lurking in the next puzzle. 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.

Also, in the contest, this puzzle was presented using arrows; instead of X < Y, it was X → Y. When transcribing to this archive, I misread the arrows and basically flipped every single sign, and got confused at how to proceed. Whoops. I'm still not entirely sure what's the best presentation, but the one I'm using right now seems to be good.

I decided I would try my hand at making another genre that was interesting and simple. Then I remembered a math problem based on this procedure, and realized the bull behavior could lead to some very interesting logic. Unfortunately, it ended up being very complicated to write in the rules, so I didn't achieve the goal of "simple". But I certainly got "interesting".

Just like how the genre was inspired by a math problem, the puzzle genre itself is also quite mathy. You need to discover a lot of theory about this genre first, but I think it's worth the journey and it will be rewarding. Good luck!

I'm not sure how likely it is to write more puzzles of this genre. The main roadblock is perhaps how difficult it is to explain the rules. Also, I'm not sure about the depth of the genre after that initial discovery. We'll see.

Some people loathe given numbers in a Skyscrapers puzzle. For me, I don't find them that big of a sin. I did try to find several alternatives, but decided this pattern was much more striking (the given numbers are the same and rotationally-symmetric!) that I decided to go with it. I love the solve path here, because it starts off completely impenetrable, and once you get the break-in (tip: the variant carries a lot of work), it becomes much more doable.

I don't remember the exact circumstances that led to this puzzle, but it likely involved Jamie Hargrove. He 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.)

First puzzle I've ever written and published, on my first blog. That said, this was published simultaneously with a few other puzzles, so was it really the first?

During my early days, I think Slitherlink was my favorite genre. For some reason I didn't immediately jump to 10x10. 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.)

My first Slitherlink at 10x10, and it had no solution (I think I transcribed something wrong). At least it was only for the first time, when I posted this on my first blog; on my second blog, when I ported all my existing puzzles over, I noticed the issue and stealthily fixed it. This is that second version. 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.

So, like the previous puzzle, this puzzle also didn't have a unique solution the first time I published it on my first blog. So, as above, I also "fixed" it when I re-published it for my second blog. But this time, the fix was also broken. So this is a different puzzle from either of the published versions. (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)

Also, this was actually also posted on the same day as the previous puzzle. I didn't want to bother with filename collision, so I just pretended this was one day later.

Yeah no the pattern is so sad.

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

Despite its size, and a note in BMPC that this puzzle is "only given once the participant has scored 150 points (out of 250) in the previous puzzles", it's still an easy puzzle. 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.

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 put this in the archive around early 2023, I remarked that Penpa+ didn't have sheep and wolves. So, I instead used shapes: white diamond to represent sheep, black diamond to represent wolf. This was motivated by the coloring of Castle Wall. The original presentation on my old blog also used diamonds, although the colors were reversed.

As you can see, now I have sheep and wolves in there. Did Penpa+ finally add them? Nope, at least I couldn't find it. These are done using text entry, inserting the sheep and wolf emojis into the cells.

Is this presentation better than diamonds? No idea. You can give it a try! Tell me which one you like better. Here's the exact same puzzle, but with diamonds (white inside, black outside): Diamond version

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. But past me actually thought this kind of use of a variant was okay. Nowadays I want to make use of 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 port 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.

A few days before this, there was a discussion in Puzzlers Club about 9x9 Regionless Star Battle. They can lead to visually striking puzzles. There might be only a small number of cells taken out, giving the impression that there are few clues and that it's difficult to break into, and yet the puzzle ends up unique and solves very nicely anyway.

I decided to try my hand on it, and this is the puzzle I wrote. The theme is that "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.

For some reason, I thought of more 9x9 Star Battle Regionless puzzles. I had an idea that I could place a 3x3 hole on the grid and that would break all symmetry. The hole isn't quite 3x3, but it's close.

Sometimes I wonder whether puzzles are invented or discovered. In many cases, they are invented, but sometimes the stars (🥁) align and something ends up unique by seemingly pure coincidence. I think this 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; there are only two ways to orient this hole. (The other orientation led to two solutions, by the way.) And just like that, the puzzle's unique without needing to do anything else. It felt like pure chance.

Apparently I posted three Sudoku puzzles here, because a (high school) friend asked me to write some puzzles. When I posted them to my blog, though, they were rife with issues: the first one had no solution, the second one had three solutions, the third one had an off-symmetry given. I apparently promised to get around to fix them, but never did.

Well, until now. This is the first one (the one originally posted with no solution), but it's now fixed. Apparently I just had to change one cell, so it was likely just a wrong transcription. Despite the small change, I found that fixing this puzzle was hard and took quite some time; there were many givens and many ways I could have made the mistake, and figuring out my original intent was difficult. (The puzzle itself is pretty easy.)

What about the other two? I feel they are embarrassing enough that I don't want to replicate them or add them to this archive. I only fixed the first puzzle so I would have space to tell this story. If you're interested to try to fix them, though, here are Puzzlink versions: the one with three solutions and the one with off-symmetric given.

Very straightforward puzzle, but the more important thing is that it's valid, and it has a pretty decent theme.

Wow, I wrote so many Irregular Sudoku puzzles for these competitions. Part of the reason was because the target audience was also pretty new and didn't know too many other genres, so I just stuck with the most well-known stuff. Not only that, but the puzzles themselves were made to be relatively easy.

I don't have much to say for all the other Irregular Sudoku puzzles, so I'll just present them without any comment.

This and the next puzzle were a pain to typeset with Penpa+. Hope you can live with this.

In addition, nowadays I feel that equations are overly general. It's pretty easy to make a huge mess with equations and make it hard to read anything. I think arithmetic-related genres want to be more restricted than this; for example, Sudoku XV (pairs of adjacent numbers that add to 5 or 10 are marked) seems like a better way to execute it.

As I said in the previous puzzle, I think this variant is kind of flawed. But it's worth to set up this gorgeous puzzle. If I were to redo the competition, I would keep this and replace the previous one with a better puzzle.

I was thinking up of new genres. At this time (December 2023), 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.

Wait, isn't this puzzle fully symmetrical— ooooh. Yeah, that was my first response too when I looked at this puzzle again.

The problem with this puzzle is that the solves for the two halves weren't sufficiently varied. Aesthetic theme like this can be extremely striking, but only if the solve paths are actually different.

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.

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.

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. I think I'm not too big of a fan of that, but it sure allows for some wacky stuff.

I'm pretty sure the "<3" rows are intended.

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 $1,000,000.

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 got something I'm pretty satisfied with, even if the URL ends up being 2000 characters long.

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 10x10 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.

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}.)

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.

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.

Fun fact: When adding these puzzles to the archive, I mistakenly extended the G one square further (overlapping the middle-left square). I only noticed that was wrong when I got to this puzzle and found that interpretation broke the puzzle.

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.

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.

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 website 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.

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. Star Battle (Regionless) in 2023 was written directly as a response of people liking the potential of 9x9 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 draw a Spheal on every cell). 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.

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.

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, here it is. Good luck!

[Zimodo's original puzzle]

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.

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.

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.

When solving this again, I was forced to use quite some bifurcation to figure out how to continue. Are you? Please contact me if you find a way to not simply bifurcate here!

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.

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. (I used this fact as a basis for the name of one of my OCs.) 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. A puzzle was posted on Grandmaster Puzzles, but I remembered its even earlier origin, in USAMTS Year 2017–2018 Round 1. It used the digits 1, 2, 3, but no reason those had to be the symbols, so 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).