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Dividing circle into parts with equal sums

Source: Kyiv City MO 2024 Round 2, Problem 7.3

February 4, 2024
combinatoricsconstruction

Problem Statement

20242024 ones and 20242024 twos are arranged in a circle in some order. Is it always possible to divide the circle into
a) two (contiguous) parts with equal sums? b) three (contiguous) parts with equal sums?
Proposed by Fedir Yudin
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