Imagine there is a 7x7 grid of lights, and only the
middle in the grid is on.
The lights are wired such that when you flip the switch for one light (from on to off or off to on) the others next to it (not diagonally) flip as well.
Using this weird wiring of lights, what is the fewest number of switch changes it takes to turn all the lights off, and which lights should you switch?
Note: Assume all the switches work in the manner explained, and there is one switch for each of the lights.
(In reply to
extension of the problem by Steven Lord)
"By requiring 4-fold symmetry (including diagonal symmetry) I reduced the number of trials by a factor of 2^4 = 16"
By doing this you discard part of the solution space, too. I know you missed a solution for size 5:
0 1 1 0 1
1 0 0 0 1
1 0 1 1 0
0 0 1 0 0
1 1 0 0 0
Note that although the initial state of just a single lit cell is fully symmetric, the solution pattern has only one diagonal symmetry.
re: extension of the problem
