Several years ago, I got a 5x5 lights out game for Christmas. It is a puzzle game in which the goal is to turn off all the lights which are on at the start (from 1 to all 25). Lights are turned on and off by pressing them. However, pressing any one light will change both that light and all the orthogonally neighboring lights.

But now, two of the lights are broken. The two lights still light up correctly, but pressing either of them will not have any effect. However, if a puzzle was solvable with all 25 lights working, it was still solvable with the two broken lights.

How many different pairs of lights can be broken like that?

All lights are on and I press the middle light; I have created a 5-square plus sign of lights off.

Let me move now to the cell directly above centre, and press that.  That light is now on as is the original, centre, one but there are four off; that above, left and right, and directly below centre.

Now, any one of the lights blanked may have a faulty activation but can be appropriately turned on by something adjacent.

The suggestion is that a pairing is needed somewhat compounds the limits of this thinking.

"Boulean", the binary "0" and "1", and operator seem to be in play.

Posted by brianjn on 2008-04-09 09:43:10