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

Created by goc3

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<a href = "https://en.wikipedia.org/wiki/Lights_Out_(game)">Lights Out</a> is a logic game wherein all lights need to be turned off to complete each board. See <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves">the first problem in the series</a> 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<pre> 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];</pre>the answer is:<pre> moves = [1 1 19]</pre>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).Prev.: <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44765">5x5, wrapping, any number of moves</a> — 
Next: <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44767">5x5, 3 stages, x moves</a>

<https://en.wikipedia.org/wiki/Lights_Out_(game) Lights Out> is a logic game wherein all lights need to be turned off to complete each board. See <https://www.mathworks.com/matlabcentral/cody/problems/44751-lights-out-1-5x5-3-moves 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).

Prev.: <https://www.mathworks.com/matlabcentral/cody/problems/44765 5x5, wrapping, any number of moves> — 
Next: <https://www.mathworks.com/matlabcentral/cody/problems/44767 5x5, 3 stages, x moves>

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

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

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