The gnomes in a circle brainteaser
A friend of mine (Neil S) recently told me about the following puzzle:
A group of n gnomes have been captured by an evil wizard. The wizard, in his twisted ways, has granted the gnomes a tricky opportunity to save themselves from a grisly demise.
The wizard has chosen n colors and he will individually paint each gnome's foreheard one of these colors. Then all the gnomes will stand in a circle, so they can see everyone else's colors, but not their own. They then must simultaneously write down a guess at their own forehead's color. If any gnome is correct (even just one), they all go free. Otherwise they will be forced into a lifetime career of unsolicited telemarketing.
Beforehand, the gnomes know what all n colors are, and they have one chance to meet to agree on a strategy. Can you think of a strategy which is guaranteed to save all the gnomes?
Just to be clear, the wizard is allowed to do strange things such as paint everyone's forehead a single color, or use only 3 colors even if there are 100 gnomes (and therefore 100 possible colors).
I should admit ahead of time that the only answer I know is pretty mathy :)
I'll post the answer in a little while.
A group of n gnomes have been captured by an evil wizard. The wizard, in his twisted ways, has granted the gnomes a tricky opportunity to save themselves from a grisly demise.
The wizard has chosen n colors and he will individually paint each gnome's foreheard one of these colors. Then all the gnomes will stand in a circle, so they can see everyone else's colors, but not their own. They then must simultaneously write down a guess at their own forehead's color. If any gnome is correct (even just one), they all go free. Otherwise they will be forced into a lifetime career of unsolicited telemarketing.
Beforehand, the gnomes know what all n colors are, and they have one chance to meet to agree on a strategy. Can you think of a strategy which is guaranteed to save all the gnomes?
Just to be clear, the wizard is allowed to do strange things such as paint everyone's forehead a single color, or use only 3 colors even if there are 100 gnomes (and therefore 100 possible colors).
I should admit ahead of time that the only answer I know is pretty mathy :)
I'll post the answer in a little while.
posted by Tyler | 6:24 PM
4 Comments:
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Great!
Thank you very much
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Go away gnomes
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