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Proof on the number of possible solutions for a jigsaw puzzle?
I was doing a jigsaw puzzle with my family and i began wondering if i could make a program that could deduce what the solution to the puzzle was by knowing what the shapes of the pieces are (4 out, 3 out 1 in ... ). This led me to thinking about the possible combinations of a puzzle if that knowledge is unknown. For example, if you had 4 peices and that's all you know, then there are 24 (4!) possible combinations. But with 9 pieces there is 8! * 4 possibilities. I was wondering if there have been any mathmatical proofs that relate to jigsaw puzzles. particularly ones that deal with the number of possible solutions.
excluding rotational symetry
1 Answer
- ?Lv 48 years agoFavorite Answer
Don't know of any formal proofs. I just want to point out that a square-shaped 4-piece puzzle would have 4!/4 combinations due to the fourfold rotational symmetry of the square. Similarly, a rectangle-shaped piece would have 4!/2 combinations due to the twofold rotational symmetry of the rectangle.