Talk:15 puzzle solver

Mathematical meaning of minimum

The meaning of minimum has been discussed see: Minimum. It means 52 not 58, assuming fewest is a synonym for minimum. I think the task description should call for 'minimum solutions to random 15 puzzles' (see below)--Nigel Galloway (talk) 10:28, 6 October 2017 (UTC)

I am surprised that anyone thinks that 52 < 31. Optimal solution improved and now linked from the task description. Pete Lomax (talk) 05:11, 24 October 2017 (UTC)

Mathematical meaning of random

Unlike minimum, which I am surprised that anyone thinks means anything other than 'reduced to the least possible amount or degree', random means easy mathematically. There are 16!/2 15 puzzles, a little over 10 trillion, of which the number that are hard to solve is counted in the hundred thousands. Therefore a randomly chosen puzzle is easy. --Nigel Galloway (talk) 10:36, 6 October 2017 (UTC)

see for an analysis of 20 randomly generated 15 puzzles--Nigel Galloway (talk) 13:00, 20 October 2017 (UTC)

that page updated with some better results Pete Lomax (talk) 05:10, 24 October 2017 (UTC)

Extra credit for non-random puzzles

We could offer extra credit for solving hard puzzles:

 2  1  3  4
 5  6  7  8
 9 10 11 12
13 14 15  0

and

  0 12  9 13
 15 11 10 14
  3  7  2  5
  4  8  6  1

--Nigel Galloway (talk) 13:08, 6 October 2017 (UTC)