Jack and Jill each have marble collections. The number in Jack's collection in a square number.

Jack says to Jill, "If you give me all your marbles I'll still have a square number." Jill replies, "Or, if you gave me the number in my collection you would still be left left with an even square."

What is the fewest number of marbles Jack could have?

(In reply to re(3): Lost their marbles (full solution) by SilverKnight)

I don't think the problem means the square of an odd number. We are originally told only that the number of Jack's marbles is a square, and that x+y is still a square, and x-y is still an even (perfect) square. If you take the problem to mean only 0, 4, 16.., using the word 'still' is out of a proverbial left field. 'Even' in this case, I still think, is only intended to mean a perfect square.

Posted by DJ on 2003-11-03 13:45:04