Three distinct 3-digit positive decimal (base 10) integers P, Q and R, having no leading zeroes and with P > Q > R, are such that:

(i) P, Q and R (in this order) are in geometric sequence, and:

(ii) P, Q and R are obtained from one another by cyclic permutation of digits.

Find all possible triplet(s) (P, Q, R) that satisfy the given conditions.

Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.

(In reply to confession, solution (computer) and an observation by Charlie)

Yes, I agree with Charlie that I was wrong to assume that P's digits were descending.

The difference between Charlie's mistake and mine was that I got "lucky" .  :-)

Posted by Steve Herman on 2008-08-27 14:10:19