IMO Shortlist 1971 problem 6


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April 2, 2012
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Let n \geq 2 be a natural number. Find a way to assign natural numbers to the vertices of a regular 2n-gon such that the following conditions are satisfied:

(1) only digits 1 and 2 are used;

(2) each number consists of exactly n digits;

(3) different numbers are assigned to different vertices;

(4) the numbers assigned to two neighboring vertices differ at exactly one digit.
Source: Međunarodna matematička olimpijada, shortlist 1971