MathDB

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.

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