Fifteen puzzle solvability, Numworks Python

[Don Shepherd]

(04-26-2020 03:15 PM)ijabbott Wrote:  There is a recent (published 2020-04-21) Numberphile video about solvability of 15-puzzle configurations, including Sam Loyd's historical 14-15 configuration.

Thanks Ian. Yes, I have seen several Youtube videos about the 15 puzzle over the years and most of them are very good. The company that manufactured that puzzle with the impossible configuration on the back should have done more research before they finalized their back cover! They should have hired me and I would have made them change it.

I love this puzzle because the solvability of a given starting configuration can be programmed easily on most programmable calculators. I have written programs to solve this on the following systems/calculators:

17bii solver
original Dartmouth BASIC
TI-84+
TI Nspire CAS
Casio FX-9860g slim
Android BASIC
HP-32sii
HP-32s
HP-71b
Casio Prizm
HP-12cp
HP-12c+
HP-65 (thanks to Dave Britten)
Numworks

As I mentioned in another post, most physical versions of this puzzle have interlocking pieces that cannot be removed from the board, and all of those puzzles therefore are automatically solvable unless the manufacturer goofed up. I have a version in which the pieces are removable, so whenever I want to mix them up and try to solve the puzzle, I always run one of my programs to verify that the particular starting configuration is solvable. Of all the possible initial configurations, only half are solvable.

Back when I was a teacher, I would do what Sam Loyd did many years ago, present a puzzle with only two numbers switched and see if any of my students could solve it. Of course, after a few minutes of failures they would cheat by physically removing a piece from the board and inserting it where it belonged!

Fascinating math.