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determine mass of all bodies with masses of 1, 2, ..., N using balance scale

Source: Estonia IMO TST 2010 p2

April 1, 2020
weightscombinatorics

Problem Statement

Let nn be a positive integer. Find the largest integer NN for which there exists a set of nn weights such that it is possible to determine the mass of all bodies with masses of 1,2,...,N1, 2, ..., N using a balance scale . (i.e. to determine whether a body with unknown mass has a mass 1,2,...,N1, 2, ..., N, and which namely).
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