This puzzle is developed by Richard Hayes. The algorithm which generates the solution to a particular board is available in Richard's technical report "The Sam Loyd 15-Puzzle".
Ken'ichiro Takahashi wrote a program to find an optimal solution of the 15puzzle.
This Java Applet was developed by Darius Cooper. Its algorithm uses a heuristic to find the best solution to the puzzle. Source code is available.
This puzzle is developed by Joseph Bowbeer. Joe wrote to us:
"I coded the first version of the solver in Prolog for Donald Michie's AI class at Univ. of Illinios in 1980. The solver's algorithm was devised by a team consisting of Philip Krause, J. O'Brien, M. Tuceiryan (and me). Since then, I've ported the puzzle to C, Pascal, and Java, making several improvements to the solver along the way. However, the solver is and has always been based on a 5-puzzle kernel operating on a set of rules developed by Donald Michie: "Preserving the Vital Link of Comprehension, PRACTICAL COMPUTING 9/79, pg 64. (Note: an error in rule 3 has been corrected here.)"
This puzzle is developed by Karl Hörnell. The graphics of this puzzle are made to resemble an actual physical puzzle.
This Java Applet was written by Alexis Drogoul. He and Christophe Dubreuil wrote the article: A Distributed Approach to N–Puzzle Solving.
This puzzle is developed by Daniel S. and programmed in Visual Basic. He explains his algorithm as follows:
- First you have to know where the piece is
- then you have to know which direction it should go (horizontally)
- get the empty space right next to the piece in that direction it should go
- move the piece that way, only touching the pieces underneath (unless you are at the bottom)
- get the empty space above (you don't have to get the empty space underneath) and move it upwards, only touching the pieces to the right (unless you are at the right edge).
- That was the basics. It exists some special cases that you have to deal with, like when you have to switch places between two pieces.
- This is the order the pieces should be moved and to which places (which is the main key that actually solves the puzzle): Piece 1 to place 1, 2 to 2, 3 to 4, 4 to 8, 3 to 3, 4 to 4, 5 to 5, 6 to 6, 7 to 8, 8 to 12, 7 to 7, 8 to 8, 13 to 9, 9 to 10, 13 to 13, 9 to 9, 14 to 10, 10 to 11, 14 to 14, 10 to 10 and piece 11, 12 and 15 to their right places.
- That's almost it! It's just the special cases you have to deal with before you're done. I hope I explained it well so you understood what I meant.
(This link is no longer available
:-(This puzzle is developed by Winston Trung-Giao. Winston has explained to me by e-mails how his solver works. He wrote: "This program try to solve it by an exhaustive search algorithm with a heuristic ( rule of thumb ) so it does not actually have to search an entire combinatorial genealogy of the solution space. Had I made it look ahead 20s step into the tree, it would have solve the problem, but this would take an enormous amount of time ( approximately 3^20th power steps). It does solve the puzzle if you can check that at least 6 to 7 square positions have fallen to the correct configuration, given 10 look ahead. This program is meant at an intro to artificial intelligence and belong to the ideas of genetic algorithm or neuro-net. Heuristic is just a first method invented in the 60's to explore possibility in thinking machine."
This puzzle is not a true 15 puzzle but it is able to solve itself. It is developed by Tony Homan. Tony wrote to us:
I have another slide puzzle with a self-solving feature. The algorithm was developed by Brian Terry, a Stanford CS graduate and lead developer at Homestead Technologies. I implemented his algorithm. The original source for the puzzle without the self-solving feature came from Java Game Programming for Dummies.