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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 ...
Behind three closed doors a car, the car keys and a goat are randomly distributed. There are two players: the first player has to find the car, the second player the keys to the car. Only if both players are successful they may drive the car home. The first player enters the room and may consecutively open two of the three doors.
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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A sliding glass door, sometimes called an Arcadia door or patio door, is a door made of glass that slides open and sometimes has a screen (a removable metal mesh that covers the door). Australian doors are a pair of plywood swinging doors often found in Australian public houses.
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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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