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MMO 174 Moscow MO 1950 3 piles from 81 weights of 1^2, 2^2, . . . , 81^2

Source:

August 6, 2019
weighingscombinatoricsalgebra

Problem Statement

a) Given 555555 weights: of 11 g, 22 g, 33 g, . . . , 555555 g, divide them into three piles of equal mass.
b) Arrange 8181 weights of 12,22,...,8121^2, 2^2, . . . , 81^2 (all in grams) into three piles of equal mass.
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