Abstract
An evil warden is in charge of 100 prisoners (all with different names). He puts a row of 100 boxes in a room. Inside each box is the name of a different prisoner. The prisoners enter the room one at a time. Each prisoner must open 50 of the boxes, one at a time. If any of the prisoners does not see his or her own name, then they are all killed. The prisoners may have a discussion before the first prisoner enters the room with the boxes, but after that there is no further communication. A prisoner may not leave a message of any kind for another prisoner. In particular, all the boxes are shut once a prisoner leaves the room. If all the prisoners choose 50 boxes at random, then each has a success probability of 1/2, so the probability that they are not killed is 2−100, not such good odds. Is there a strategy that will increase the chances of success? What is the best strategy?
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Stanley, R.P. (2013). Miscellaneous Gems of Algebraic Combinatorics. In: Algebraic Combinatorics. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6998-8_12
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