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$n$ is circular

Source: May Olimpiad 2020 L2 P5

November 27, 2020
number theory

Problem Statement

We say that a positive integer nn is circular if it is possible to place the numbers 1,2,⋯ ,n1, 2, \cdots , n in a circumference so that there are no three adjacent numbers whose sum is a multiple of 3. a) Show that 9 is not circular b) Show that any integer greater than 9 is circular.
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