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TOT 053 1984 Spring J-O1 S-O1 Humpties and Dumpties price

Source:

August 19, 2019
algebracombinatorics

Problem Statement

The price of 175175 Humpties is more than the price of 125125 Dumpties but less than that of 126126 Dumpties. Prove that you cannot buy three Humpties and one Dumpty for (a) 8080 cents. (b) 11 dollar.
(S Fomin, Leningrad)
PS. (a) for Juniors , (a),(b) for Seniors