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Just in case you missed it, here's the original puzzle. Suppose we have n=2 gnomes, and the possible hat colors are red and blue. Gnome 1 (G1) can always guess that his hat is the same color as gnome 2's hat; while gnome 2 (G2) can always guess that her hat is the opposite color as gnome 1's. We can check each possible placement of hat colors to see that, in each case, one of the gnomes correctly guesses his/her own hat color. A green highlight indicates a correct guess of a gnome's own hat color.
This is a solution for n=2. Once you've thought about this for long enough (don't just give up!) you should check out this solution to the puzzle. |