The puzzle is similar to the Magic Squares puzzle. The rules for right box in the puzzle I'm thinking about are:1 - A click on the corners changes the state of the corner and the two adjacent edge squares.
2 - A click on the center changes the center and all 4 edge squares
3 - A click on an edge square changes that edge and the two adjacent corners.
I currently have the following algorithm which has solved every attempt I have tried:
Correcting a square is when you check if it matches it's corresponding square in the left box, and if it isn't you click it to make it match.
1 - Since the center can only be changed by clicking it, correct it.
2 - Correct all four corner squares while ignoring any edge squares you change.
3 - Correct all the edge squares while ignoring the changes you make to the corner squares.
4 - Repeat steps 2 and 3 until the two boxes match.
However I'm wondering if there are any algorithms that can solve any initial states with less clicks. Since there are only two states for each square clicking the same square twice is effectively the same as not clicking it at all. With this and the order of clicks not mattering all initial states should be solvable in 9 clicks at most. But I currently have no idea how I could go about finding which squares need to be clicked.
Printer-friendly copy
Email this topic to a friend
