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11 March 2010 @ 10:10 pm
Friday Puzzle #40 - 2010 Kakuro  
Rules: Place a single digit from 1 to 9 in each cell so that the sum of each horizontal/vertical group of cells equals the number given immediately on its left/top side. Digits cannot repeat in any answer.

The 2010 project was inspired, in part, by a fold-out Kakuro in the Giants 7-12 compendium by Nikoli that I got for Christmas. It had a clear 2000 theme in the large black square pattern, with the requisite mirror symmetry in the grid for a kakuro, and open shapes for the 0's since the white cells must all be connected. However, besides the black square pattern, I can't remember anything specific about the solve today except that I beat the fastest time standard by a dozen minutes [I average about 85-90% of that time standard on kakuro on paper and while this time standard is never used on Nikoli.com, I'm probably only marginally faster there and well behind the H.Jo's and Ziti's of the world].

In part, the lack of puzzle memory reflects the fact most kakuro puzzles aren't particularly distinctive in their steps or theming. Some of the grid designs are pretty nice, and do have a much higher hit rate than the crossword, but few are indelibly stored in my mind. Regarding themes encountered during the solving process, I can remember a few that had a 123456789 answer to a 45-clue revealed during the process, and a couple easy ones that used only the digits 1-5, say, or that had a "small" half and a "big" half where opposite corners were using the two-cell 3/4 and 16/17 clue intersections standard for those ranges. Probably the most memorable design elements have been the kakuro that use a very minimal number of clue values in a particular region and exploit their interaction in clever ways. A quick example is a region with only 4-cell long clues which are all interlacing horizontal and vertical 10's and 11's which manage to pass a message in the unshared 4s and 5s away from the shared 123 cells. One of the large fold-out kakuro I did I think had regions with something similar like 5-cell 34s and 16s that fed chained 4/6 information together and separated 123 and 789. Aside from these few cases, most kakuro are completely forgettable and I feel I enjoy solving them more to time myself against the printed standard rather than to discover something new.

This lack of intrigue in most kakuro may also be why I've now written over a dozen kakuro variants (including some of my earliest puzzles posted on this blog and some of my better Mystery Hunt puzzle constructions/co-constructions) but absolutely no "classic" kakuro. New rules inevitably lead to new discoveries for the solver, and achieving the same in a "classic" puzzle would require much more skill.

Anyway, the 2000 kakuro in the Nikoli magazine got me thinking on my flight home about types of puzzle theming and meshing aesthetic elements with logic elements; I decided I should try to make some "normal" puzzles this year in types I'd never really written before, and explore different ways to take an "obvious" theme and present it in each type. Thus, the 2010 project. After tackling many other types and having some successes and failures, I figured it was time to finally return to the setting that catalyzed my initial thinking. I didn't want to make a particularly large kakuro, or repeat the embedded 2010 theme in black squares as I'd seen done in that puzzle from 10 years ago. Instead, I decided to try to maximize 20 and 10 clues in the puzzle. This isn't the easiest set of digits to use a ton of times but its not terrible. 16 is probably the single best clue value for such a task, since it can represent four clue lengths and also has a fixed 2 and 5 cell number set; 15 and 17 are the next best, each still cluing two to five cell answers with one perfectly fixed set in each case. 20 and 10 are pretty good with the most notable distinction being the different clue lengths each can fulfill. The four-cell 10 is a well known set but summations of 20's are not as common, so I also wanted to explore a lot of ways to get to 20 and demonstrate the use of different clue lengths to create interactions between 20's and 10's. For a couple hours I just played with different grid designs and sizes to see how to situate symmetric clues that allow 20's and 10's to work together. I coalesced around the three stripe design, and then spent a couple more hours working out how to maximize the 20 and 10 clues in the puzzle, with "other" clues only on the periphery and minimized as much as possible. I'm pretty proud of the result, but it is a hard puzzle to solve. Enjoy - and feel free to share your memories of kakuro past if you think I'm selling the puzzle type short.
(Anonymous) on March 12th, 2010 06:10 pm (UTC)
I'd generally agree with your comments about Kakuro. I'm always rather disappointed when it comes up in the rotation on Nikoli.com. (BTW, sort of psyched to see that they are adding Yajilin, though having some sort of "dot" marker for "there's some sort of path in this square but I don't know which way it points yet" might make the computer interface better.)

Your 2010 themed kakuro today does about what anyone else does that's interesting -- creative ways of using the 20's and 10's, the required crossword symmetry and so forth, and a nice logical solving path. I think the most interesting thing for me was realizing just how constrained some of those 5-cell 20's got to be once you had just a little more information about them. Definitely a challenging puzzle, but not unfairly so, and not requiring long complicated chains of thinking ahead.

- Jack
motrismotris on March 12th, 2010 06:13 pm (UTC)
So I'm not as psyched for Yajilin as its hard to solve on the computer interface and I'm getting black squares on my loop squares by bad clicking. Still, a shift click does the dot thing you want to do.

I really liked the work-in I gave in the second column, and then some of the constrained 5-cell 20's exactly as you said. One particularly good one becomes a 10 after you fill in two digits and leaves just one choice for the remaining three.
thesubro on March 12th, 2010 06:19 pm (UTC)
"lack of intrigue in most kakuro"
In the words of the great Tom Snyder: "lack of intrigue in most kakuro."

In my meager words "lack of interest in ALL kakuro."

Thanks for the effort, but you can't make us like liver no matter how you dress it up.

lardarsegreg on March 12th, 2010 08:41 pm (UTC)
I think that, for me, Killer Sudoku is the best of both worlds between "vanilla" Sudoku and Kakuro, and that both of the component parts feel a little weak by comparison when compared to it. Sudoku at least has ways of being interesting without relying on gimmicks (although for me it tends to feel horribly inelegant when I have to fill in all of the candidates just to find a single that I'm not able to see). Kakuro, on the other hand, usually feels like a lot of effort for very little reward (which for puzzles like these, tends to be just the satisfaction of solving it; but even that can be motivation enough to keep going with a puzzle)...

Now, I'm probably selling it even shorter than you have done, given that I've tried very few of them (because I've found the ones that I have tried somewhat boring - a vicious cycle, admittedly), and I don't think I've ever tried one that is "Nikoli standard", but I'm willing to have a go at this one. Hopefully, I'll find time to try it this weekend...
(Anonymous) on March 15th, 2010 12:36 pm (UTC)
I don't know whether I'm feeling a little slow today, but I found this a little fiddly - I had to spend a couple of minutes pencilling in a few candidates to see where the logic went for at least a couple of cell interactions. This is typical of some of the harder newspaper kakuro you get here.

More interestingly, I think this is the first kakuro I've thought to use cage addition (though I couldn't say whether this was 100% necessary in this puzzle). It's something you normally associate with killers, although I'm not a fan of it at all, and when I made that killer the other week, having a puzzle in which cage addition was entirely redundant was top priority. Generally I prefer killers that feel more like kakuro as I do enjoy kakuro!

The best kakuro in my opinion are the ones which don't overdo the obvious combinations, but still give you a flowing sensation as you traverse the grid. In particular, they ought not be too "fiddly", instead the process of initially filling out the "gimme" clues should reduce very ambiguous clues into the overdone clues without having to hunt around too much (c.f. requiring things like swordfish, x-cycles and the like for a sudoku). It's this distinction I've sort of waffled here that I feel is the difference between newspaper puzzles and the ones I see on nikoli.com.

zundevilzundevil on March 29th, 2010 06:13 pm (UTC)
I've been meaning to comment on this and shall now. I like kakuro -- no surprise there. But I'll admit, it doesn't have hardly any of the nifty trick you find on most of the other variations. There's no real global communication, there's only so many ways to fill in a given Y-in-X combination, and the only way to make a puzzle more difficult is to increase its size (for the most part).

Someone who reads this blog (I think) once pointed out that Nikoli puzzles were less satisfying than those from (shudder) Dell Magazine. I dunno if that's my attitude in particular, but they definitely serve different roles. All things considered, the "fiddly" puzzles from Dell can be significantly more difficult and lack any semblance of elegance...but at least you have to work (sometimes hard!) to get the solution. That's more pleasurable than another 2min assault on a 19x11 Nikoli one.

Conceptis put out a "Black-Belt Kakuro" book that I found very pleasing a few years back. And the puzzles near the end of the Nikoli books can be pretty doggone difficult while not feeling like the grind of the Dell ones. The occasional 31min (expert-time) Nikoli puzzles are probably the best ones going.

Aside from these one-offs from Thomas, of course.