Let
be a natural number. Find a way to assign natural numbers to the vertices of a regular
-gon such that the following conditions are satisfied:
(1) only digits
and
are used;
(2) each number consists of exactly
digits;
(3) different numbers are assigned to different vertices;
(4) the numbers assigned to two neighboring vertices differ at exactly one digit.
![n \geq 2](/media/m/2/1/f/21fe2458de6d1580c44fd06e0fac11bb.png)
![2n](/media/m/d/2/d/d2da874dc9bc356be9468cdbd57fbfdf.png)
(1) only digits
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
(2) each number consists of exactly
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
(3) different numbers are assigned to different vertices;
(4) the numbers assigned to two neighboring vertices differ at exactly one digit.