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10 votes
1 answer
1k views

How do I determine whether a 5x5 Lights-Out puzzle is solvable without trying to solve it?

The following two 5x5 Lights-Out puzzles are not solvable. Is there a way to find out why, without trying to solve them? [1, 0, 0, 1, 0] [1, 1, 1, 1, 0] [1, 1, 1, 0, 0] [0, 0, 1, 0, 0] [1, ...
Apostolos's user avatar
  • 201
6 votes
3 answers
1k views

Flipping coins in a circle

We have a set of N coins that are all placed in a circle. They all have "Tails" as their face up side. The coins are all distinct and have numbers (1,2,3...N) written on them. In each move, ...
Hemant Agarwal's user avatar
3 votes
1 answer
172 views

Fill 5 x 5 grid

In each cell of a 5 × 5 square there is a token that is black on one side and white on the other. Initially all tokens are placed with the white side facing up. On each move three tokens in ...
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