## Arithmetic Ring

#### Problem

The digits 1, 2, 3, 4, 5, 6, 7 and 8 are placed in the ring below.

With the exception of 6 and 7, no two adjacent numbers are consecutive.

Show how it is possible to arrange the digits 1 to 8 in the ring so that no two adjacent numbers are consecutive.

#### Solution

Here is one solution.

Are there any more solutions?

What if you had to arrange the numbers 1 to 12 in a 4 by 4 ring?

How many numbers would there be in an `n` `n` ring?

Problem ID: 117 (May 2003) Difficulty: 1 Star