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Question: special disks say you have a set of special disks...

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Special Disks: Say you have a set of special disks with numbers on them. There are 15 people sitting at a round table, and each person has two disks. One of the numbers 1,2, 3, 14, 15 is written on each disk, and each number occurs on exactly two disks. Each person passes one of his or her disks-the one with the smaller number to the right. Prove that, sooner or later, one of the people will have two disks with the same numbers.
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