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166

Part of 1949 Moscow Mathematical Olympiad

Problems(1)

MMO 166 Moscow MO 1949 13 weights of integer mass

Source:

7/20/2019
Consider 1313 weights of integer mass (in grams). It is known that any 66 of them may be placed onto two pans of a balance achieving equilibrium. Prove that all the weights are of equal mass.
weighingscombinatorics