Consider a 3x3 array of lighted buttons:

[O][O][O]
[O][O][O]
[O][O][O]

If any one of these buttons is pressed, it and all of its directly adjacent neighbors will toggle their status on/off. (Diagonals do not change.)

The goal is to get all of the lights to be off. Which buttons must be pressed to accomplish this?

Which buttons would accomplish this goal in the minimum number of presses for 4x4, 5x5, 6x6, 7x7, 8x8, and 9x9 arrays?

A nice site with the game from 3 x 3 up to 8 x 8 is here.

(In reply to computer solution by Charlie)

That is a nice program.  Would you mind increasing the size of the grid?  I only stopped at 9 because that's how far I got by hand.

You could also alter the program to rule out symmetrical results by looking at the first and last rows as binary numbers and seeing if they are the same.  The last row being read backwards.

Posted by Jer on 2009-06-04 11:51:06