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When I was growing up, I had a subscription to Games magazine. It’s a puzzle magazine whose main feature is the “pencilwise” section that takes up the middle chunk; crosswords are always most prominent in that section, but they’re always in a minority, with a wide range of other puzzle formats keeping them company.

Lots of fun; one fallout that I particularly remember was having my desk moved by a high school science teacher (who also happened to be my mother) because a friend of mine and I kept on talking about cryptic crossword solutions. I let my subscription lapse when I went away to college, though, since I had more than enough else to keep me busy.

I would still look for copies when I was traveling, however, because it’s a perfect accompaniment for a plane trip. And new puzzle varieties appeared in its pages over the years; Liesl and I both went through a big Paint by Numbers phase, for example. But one trio of new puzzles caught my eye in particular: Nurikabe, Masyu, and Slitherlink. Unlike crossword puzzles, they’re pure logic puzzles, not depending on any sort of outside knowledge; unlike Sudoku, your solution largely develops locally, so if you discover you’ve made a mistake, you can usually fix it without having to start over from scratch. They all develop in a wonderfully organic fashion, with tendrils starting in various places on the puzzle, and slowly extending until they’ve all met and completed the puzzle.

Eventually, I noticed that Games magazine got all of those three puzzle types from the same source, namely Nikoli. Which is a Japanese company, so I couldn’t find their books in American stores; I poked around, though, and found a few other sources of Nurikabe puzzles. Which proved to be a disappointment: the solutions just didn’t unfold in the same organic way as the solutions to Nikoli-authored puzzles did. So it’s not just the rules of the puzzle that matters: even though it’s a puzzle of pure logic, the author makes a real difference.

At some point, I had enough different Japanese products that I wanted that I couldn’t find in the U.S. that I figured I’d order from Amazon Japan; and I threw a few Nikoli books into the mix. And I’m very glad I did: if you order enough stuff to spread out the worst of the shipping costs, they’re actually quite cheap, contain dozens of hours of entertainment, and even fit into a jeans pocket in a pinch. (Which is convenient if you’re on a trip, if you naturally go through museums slightly faster than your travel companions, and if you have to check your backpack.) I had great fun going through the nurikabe and masyu books that I ordered, didn’t like another one (Numberlink) so much, and was enjoying slitherlink.

But even though I was enjoying Slitherlink, I wasn’t at ease with it in the same way as I was with Nurikabe and Masyu. My solutions to the latter ones unfolded smoothly (honestly, to the extent that they’re a bit easy, though never unpleasant), whereas with Slitherlink, I was constantly getting stuck and having to search all over for my next move. It got bad enough that, when trying and failing to do the last puzzle in the second (of four) sizes in the book, I was ready to give up: the puzzle was taking me ages, I was reading possibilities ahead hoping in vain for contradictions, and I just wasn’t enjoying myself any more; and the larger sizes ahead of me would just exacerbate those problems.

Out of stubborn pride, though, I decided to take one last swing at finishing that puzzle. I gave up all sense of shame, and marked down on the puzzle every little thing I knew: if a square was marked as a zero, I would dutifully put little x’s on all four sides, even though it was obvious that lines couldn’t go on those sides. And, in doing so, two surprising things happened: for one thing, I noticed several places where I hadn’t noticed that I could apply simple rules (instead of searching in depth). And, for another thing, I discovered several new consequences of the rules! As the text version of the rules says,

Its greatest feature is countless theorems. Experience the feeling of getting much skilled when you find new theorem.

Which I’d mostly decided by that point was puffery: yes, I’d found three or four theorems, but it had been ages since I’d found any more, surely I’d found all there were? Apparently not, and, as became clear as I proceeded further through the book, I wasn’t even particularly close to discovering all the useful theorems.

And wow, what a puzzle form Slitherlink turns out to be, to the extent that it’s now my favorite logic puzzle format. Which is due to two reasons, namely:

• It balances local and global requirements.

The main lesson I’ve learned from the Nikoli games is that I like puzzles where I spend most of my time figuring out what’s going on locally, but where the puzzle has just enough of a global constraint to give an overall structure.

Slitherlink is a fine example of that: the rule that each numbered square tells you how many sides are filled in is purely local, and while the rule that the solution forms a single loop looks global (and is, of course), it has a few immediate local corollaries, namely that you can’t have dead-ends, branches, or tiny loops. Because of this, I can spend time developing a front, I can move from one front to another if I get stuck, I can (usually) only erase a portion of the puzzle if I find I’ve made a mistake, and I can occasionally get surprised by looking at the whole puzzle and realizing that my next move is forced by a large loop that is almost closed.

• The balance between following mindless rules, higher-level rules, and exhaustive search.

This one is a little more subtle. Any puzzle has rules, which frequently directly force your move. And any good puzzle is going to have situations where you just have to read out the consequences of options, hoping to find a contradiction before you get too far.

But if you do too much of the former, you get bored; if you do too much of the latter, you get frustrated. And what Slitherlink shows is that there’s a third choice: there are constraints that are true but not immediately obvious from the game’s rules. As you discover this, your rule-following behavior becomes richer (because there are more patterns to recognize), and your exhaustive search also becomes richer (because you can search more deeply, with the help of these extra rules to prune your search). And, in a further reward loop, you can occasionally systematize the result of an exhaustive search in the form of a newly-discovered higher-level rule.

Most of the puzzles in the second half of the book took me more than an hour to solve, and I’m sure several took me more than two hours to solve; normally, that would be a sign that I’m banging my head against the wall in frustration, but not this time. I’m sure that, as I work through further Slitherlink books, the puzzles will become more routine, and I’ll be looking for something new, but for now it’s great fun.

(Incidentally, my main takeaway from the iPad launch: I really hope that Nikoli produces games for that device. They have some Akari puzzles for the iPhone, which I highly recommend, but the iPhone is too small for their richest puzzles; the iPad could be a perfect device for those puzzles, though.)