Imagine there is a 5x5 grid of lights, and only the middle light 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 right 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? (Assume all the switches work in the manner explained, and there is 1 switch for each of the lights.)

(In reply to re(2): First steps to proof by rerun141)

hmm... oh yeah. for the 2 by 2 square i just put the x to the top left. There, you can flip that switch on to make it

O X

X O

then flip the bottom right off making it.

O O

O X

then flip the top left again.

X X

X X

Oh yeah, after thinking it a bit more this "can't" happen because x is not in the center for there is no center in a y by y square if y is even.

hmm.. so the only grids that have centers that work are 1x1 and 3x3 my bad :P
Edited on November 2, 2003, 5:18 pm

Posted by Victor Zapana on 2003-11-02 17:16:50