Three 3-digit positive base N integers P, Q and R, each with no leading zeroes and having the restriction P < Q < R, are such that:

• Q is the arithmetic mean of P and R, and:
• P, Q and R can be derived from one another by cyclic permutation of digits.

Determine all possible positive integer values of N < 30 for which this is possible.

(In reply to Cycling Backwards (spoiler) by Harry)

Right you are, Harry!  Proving once again that three answers are better than 2!

Posted by Steve Herman on 2009-06-10 01:18:16