Thursday, February 26, 2009
Berlekamp's Switch Game
The game has 100 bulbs, 10x10. Each row and each column has a switch that turns off bulbs that are on, and turns on bulbs that are off. Can you turn off all the bulbs?
The answer, even if you do attempt every possible combination, is no. But according to Microsoft Research, there's a way to "solve" the puzzle to within 1%, even if the board had 1000000 bulbs. The funny thing is, the algorithmic solution to the puzzle (originally built by Elwyn Berlekamp in 1960) can be used as a way to bypass brute-force computing in solving problems. The researchers at Microsoft are more interested in that whole thing, but I'm more interested in how some guy got to build this nice electronic board game as part of his day job, just for Show and Tell. Way to go, dude.
Here are the rules, in case you want to make your own home version (Phil Torrone, do you hear me?):
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