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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 times n ring?

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

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