Each of P, Q, R, S and (P+S), with P < Q < R < S, is a non leading zero 10-digit base ten positive integer containing each of the digits from 0 to 9 exactly once. It is known that R is the arithmetic mean of P and S, and Q is the geometric mean of P and S.

Determine the minimum value of P and the maximum value of S.

(In reply to re: Considerations which might reduce programming by Charlie)

Dazzled by convenience!!!

"Why must P and S be perfect squares?"

two numbers that are not perfect squares can multiply out to a perfect square

The above two italicised comments are made regarding an earlier post by me.  The data derived from the program mentioned in one of my comments was very convenient and fitted the stipulations of K Sengupta.  Unfortunately they are just one set in the possible considerations as Charlie points out by way of the second comment.

This example indicates why P and S do not have to be squares as was previously considered:
If  P = 2 and S = 32 then Q = √64 = 8.

So ...  no closer to finding a convenient programmed algorithm!

Edited on July 23, 2009, 11:00 pm

Posted by brianjn on 2009-07-23 22:59:57