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Find a way to assign natural numbers - ISL 1971

Source:

September 22, 2010
combinatoricsGraph coloringconstructionIMO Shortlist

Problem Statement

Let n≥2n \geq 2 be a natural number. Find a way to assign natural numbers to the vertices of a regular 2n2n-gon such that the following conditions are satisfied:
(1) only digits 11 and 22 are used;
(2) each number consists of exactly nn digits;
(3) different numbers are assigned to different vertices;
(4) the numbers assigned to two neighboring vertices differ at exactly one digit.
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