Chess Visualization & Calculation By 15 Puzzle
Chess Visualization & Calculation By 15 Puzzle
I recently watched some of the Carson Tonight Show with host Johnny Carson and guest GM Bobby Fischer. This originally aired 1972, November 8. I loved the interview and was fascinated at how quickly Fischer solved the 15 puzzle.
(I’ll leave the YouTube hyperlink here: https://www.youtube.com/watch?v=QxvnEwvgfeI )
For those unaware, a 15 puzzle (also goes by other names such as “Magic Square”, “Gem Puzzle”, “Game of Fifteen” and several other names) is a children’s game. A 4x4 grid of movable tiles are labeled “1” through “15” (sometimes a picture is used instead of numbers) and one “space” exists with no tile. The object of the game is to shuffle the tiles to “reset” the puzzle and then try to re-arrange the tiles in the correct order:
Top row: 1-4
Next row: 5-8
Penultimate row: 9-12
Bottom row: 13-15 and the black “space” at bottom-right.
Competitive measures of this game typically time how fast the player can solve this puzzle although alternatively, sometimes players instead measure by solving in the least number of “moves.”
Before watching this interview, I will note that I personally was never good with these types of puzzles in my childhood. Board games and especially strategy games, yes! Trying to solve puzzles like the Rubik’s Cube would frustrate me after ten minutes though. I excelled at jigsaw puzzles, but my problem with these games is that I’d “solve” everything correctly and then have one tile in the wrong spot and not know how to finesse it to the complete other side. Naturally, there are “tricks” (algorithms and heuristics) that can help; without knowing these by memory, these were always challenging for me to solve.
At least for my childhood friends, solving a 15 puzzle typically took 5 minutes or so. I never really got into it much. In the interview, Fischer casually states, “[Carson: “Is that very difficult?”] “Nah, it is very easy…I’m the fastest in the world at this, I don’t like to boast [audience chuckling at his blunt humor].”
Upon asked how quickly he could solve this, Fischer explains, “Well this is not really a nice oiled up set, so it might take me 30 seconds or so [met by light laughter thinking this is a joke].” Fischer then adds, “A real good set, I could probably do in about 20.”
On stage, they time Fischer and it takes him 17 seconds to solve! Naturally, the audience begins clapping and Carson just observes stunned as the comedian he is.
I became motivated to try the 15 puzzle myself and see how close I could get to Fischer’s speed; I’d be satisfied with anything under 2 minutes. I tried several online 15 puzzle sites, but the one I liked best I’ll leave the hyperlink for here:
I figured this game might indirectly help my chess by helping refine my visualization and “calculation” ability.
My first attempt I had no instruction and I just went for it. I solved it in about 15 minutes; just like I had remembered, I’d solve the first few numbers correctly and then have trouble getting one or two annoying tiles where they belong.
I then looked up some tutorials and tips online for it and spent the next hour or two solving that same night. My times varied in the range of about 10-20 minutes per attempt - most of them being about 15 minutes. The following day, I continued the practice and brought my average solving time down to roughly 8-10 minutes per attempt.
I didn’t really forget about the 15 puzzle, but the next few days I didn’t try it for one reason or another. I tried again several days later and my average was hovering around 5 minutes now! Determination refueled, I grinded a few more attempts that day and began averaging 3-4 minutes.
After about a week since I watched Fischer solve the puzzle, I was now scoring times close to 1 minute! Every now and then I might score 2 minutes, but occasionally I’d solve it within 45 seconds.
My record now is exactly 30 seconds! This is really close to Fischer’s 17 seconds solved on stage. I’m simply amazed at my swift progress with 15 puzzle, but now I’m even more content at the fact I feel this experience has slightly improved my chess visualization and calculating as I similarly can visualize where to transfer the tiles in 15 puzzle. This is a great little exercise to help in chess improvement if one seeks a change of pace from traditional chess methods.
