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Part of 2000 Bundeswettbewerb Mathematik

Problems(1)

We can divide weights to 3 groups [Germany BW 2000]

Source:

n \geq 3

weights of masses

1, 2, 3, \ldots , n

grams. Find all

n

for which it is possible to divide these weights into three groups with the same mass.

combinatorics proposedcombinatorics