Friday Puzzle #40 - 2010 Kakuro
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.