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TH-TMO 2018 Problem 3

    Karakade has three flash drives of each of the six capacities 1,2,4,8,16,321, 2, 4, 8, 16, 32 gigabytes. She gives each of her 66 servants three flash drives of different capacities. Prove that either there are two capacities where each servant has at most one of the two capacities, or all servants have flash drives with different sums of capacities.

    Dataset text AI-MO AoPS. Quoted with source.

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