Problem 44766. Lights Out 12 - 5x5, three stages, <7 moves

Lights Out is a logic game wherein all lights need to be turned off to complete each board. See the first problem in the series for an introduction.

This problem is back to no wrapping and contains boards that each require six or fewer moves to solve. However, now lights are activated through three stages, rather than two, cycling from on1 (1) to on2 (2) to off (0). For example, if

 board = [1 1 0 0 0  
          1 0 0 0 0  
          0 0 0 2 0  
          0 0 2 2 2  
          0 0 0 2 0];

the answer is:

 moves = [1 1 19]

since the first "1" will change the 1's in (1,1), (1,2), and (2,1) to 2's. The second "1" will then change those three values to zero, while the "19" will bump the five 2's to zero. Therefore, up to two moves are possible for each button (index).

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