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Dollars, Purses, and Pockets

Source: Tournament of Towns Spring 2003 - Junior O-Level - Problem 1

June 14, 2011
combinatorics proposedcombinatorics

Problem Statement

20032003 dollars are placed into NN purses, and the purses are placed into MM pockets. It is known that NN is greater than the number of dollars in any pocket. Is it true that there is a purse with less than MM dollars in it?
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