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One guard always lies and the other always answers truthfully. One door leads to the castle and the other leads to 'certain death'. The puzzle is to find out which door leads to the castle by asking one of the guards one question. In the movie, the protagonist does this by asking "Would he [the other guard] tell me that this door leads to the ...
If the car is behind door 1, the host can open either door 2 or door 3, so the probability that the car is behind door 1 and the host opens door 3 is 1 / 3 × 1 / 2 = 1 / 6 . If the car is behind door 2 – with the player having picked door 1 – the host must open door 3, such the probability that the car is behind door ...
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Trapdoor puzzles - the 3 must open or close all of a set of doors; clicking on one door will toggle the open state of several others, with the exact set of doors, toggled depending on the state of the door clicked. (Thus clicking on door 3 may open or close doors 1, 3, and 9 if it is open, but 3, 4, and 5 if it is closed.) Reordered word ...
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A 3-coloring of the vertices of a triangulated polygon. The blue vertices form a set of three guards, as few as is guaranteed by the art gallery theorem. However, this set is not optimal: the same polygon can be guarded by only two guards. Steve Fisk's proof is so short and elegant that it was chosen for inclusion in Proofs from THE BOOK. [4]
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