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.)

4 clicks.
0=off, 1=on.

start:
00000
00000
00100
00000
00000

click at pos.1:
11000
11000
00100
00000
00000

Click pos. 6;
00000
00000
11100
00000
00000

Click pos. 17:
00000
00000
00000
11100
11100

Click pos. 22:
00000
00000
00000
00000
00000


There's four clicks that solve the problem. No programming necessary, just some pen & paper. If I 'm supposed to come up w/ some sort of formula, I'll fail miserable around here. I'm just good at puzzling.

Posted by Choop on 2003-11-03 01:12:10