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?
If we call the number of marbles Jack has
x, and the number of marbles Jill has
y...
then the problem says that:
- x is a square number.
- y + x is a square number, and
- y - x is an even square number.
y -
x must be positive (because it leaves "an even square"), and therefore Jill has more marbles than Jack.
Jack having
zero marbles, and Jill having
four marbles will satisfy these requirements.
But if Jack must have non-zero marbles, then his having
16 marbles and Jill having
20 marbles will also satisfy these requirements.
Edited on November 3, 2003, 10:08 am
solution
