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Gathering of Engineers

Ludographic considerations from the Silicon Forest

Monday, September 12, 2005

Positively Puzzling

Alright, this is the week I get all gushy, especially with Tom Vasel's call for positivity, so I'll talk about something I have loved for a long time. With a toddler in the house, my gaming hours have dropped considerably this year. One of the things I have used this extra free time for is one of my oldest hobbies: pencil puzzles. My preferred format is the magazine; currently, the GAMES line is best, with Dell dropping off sharply since the early 90s, when they had the Champion Variety line and some charming yet brutal 5-star entries in their Logic Puzzles issues. There is a worldwide surge in interest in clever logic puzzles; Conceptis Puzzles alone has 40,000 registered users, and I imagine that Puzzle Japan well surpasses that, given the country's strong fanbase. Most surprising is the Suduko phenomenon. Sudoku is a fairly dry puzzle which has been around for decades under less exotic names; I would have been less surprised to see gangs of Diagramless Crosswords solvers hanging out at the light rail stations.

To me, the most interesting thing about these types of puzzles is that they are all solvable using brute force (i.e., just try all the possible combinations), but efficient solving techniques involve different styles of hard thinking. The type of thinking done depends upon both the difficulty of the puzzle and whether you are attempting to solve the problem quickly. I am somewhat obsessive-compulsive in that, if I accidentally stumble upon the solution while exploring a search branch, I will usually take the extra time to prove the solution is unique. In the past, I participated the U.S. qualifying round of the World Puzzle Championship, with my best finish being 3rd in the 2000 qualifiers. In recent years, some of the performances have been incredible (see the typically sharp dropoff in this year's results). Given the difficulty of the problems and the time limit, I suspect that the top solvers aren't simply superfast thinkers that can quickly prune the search tree and identify pieces of the solution; rather, their experience with these puzzle types has honed their intuition, and that they are now excellent at guessing which branches to explore. For example, in Conceptis' Fill-a-Pix puzzles, experience will show that a chain of 4s and 5s is almost always used to draw an easily predictable curve.

In board games, sharp tactical thinking is required to find the lines that are most lucrative in the short-term, while strategic thinking is useful for evaluating positions when thinking deep. I have soloed four-handed matches of Tongiaki 20+ times to help hone heuristics for the opening, hoping to find a feasible strategy for the later seating positions. With the social pressure to play multi-player board games at a fairly brisk pace, and the various random elements most of these games have, heuristics are key if winning is desired. Of course, two-player abstracts are rich with heuristics, with one of my current favorites being YINSH; Alan Kwan tells how we won the 2004 World Championships under intense time limitations - 15 minutes per player!

Here is a list of my favorite online solving sites:

Conceptis Puzzles has weekly online puzzles for three varieties. Pic-a-pix (another international craze known more familiarly as Paint-By-Numbers) puzzles come in larger sizes than those in magazines, and often feature many colors, but I find the end result being way more tedious than the magazine variety. On the other hand, the Fill-a-pix and Link-a-pix online versions are much less tedious, and scale well to the larger sizes. Since the new puzzles are released on Sunday nights, I will probably struggle at times to meet my Monday blogging deadline!

PuzzleBeast hosts a variety of challenging puzzles created by a Java program. Spend some time struggling with the devilishly simple Sliding Block Puzzles, then complete the humiliation with the ConSlide Puzzles. More accessible are The Bulbous Blob Puzzles and The Kung Fu Packing Crate Maze (which I saw in the local game store today packaged as TipOver).

Clickmazes has more puzzles along the lines of PuzzleBeast, with a less snazzy interface but a wider range of difficulty and opaqueness in the puzzles. For starters, try the classic Plank Puzzles, Full-Houze Puzzles, or the Tilt Puzzles.

Puzzle Japan is, to the best of my knowledge, the only full-fledged pencil puzzle site with a subscription fee. While their variety includes many familiar puzzle types I am not crazy about (including Sudoku), they all demonstrate that web interfaces are excellent for these types of puzzles. The sample problems for Nurikabe, Slither Link, and Light Up almost convince me to sign up, if only to support such an effort.

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