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(5): Lost their marbles (full solution) by SilverKnight)

That's a rather presumptuous statement, and I'm still pretty sure that simply a perfect square was intended, whether it was intended or not. It is rather common to see usage such as an 'even integer,' an 'even factor,' or an 'even square' intended not to mean divisible by two, but exact or precise.

As you put it so well, "every number is a square (of something)" and saying an 'even square' in this case clarifies that a perfect square is what we are looking for.

Based on the context, if Jack started with any square, and after giving Jill marbles he still had an even square, to say that it is still divisible by two would not make sense, since that wasn't a condition in the first place.
By your own logic, if he intended 'even' to mean divisible by two, he would have included the word 'even' in the OTHER two references to a square number in the problem.
Perhaps, then, 'even' isn't the best word to have used, but I think it was perfectly clear to everyone else what was intended.

Anyway, I'm done discussing it; Ravi can tell us what he meant, as opposed to your prematurely bold declaraion of what he did mean and would have said, since you would of course know his exact thoughts when writing the problem.

Posted by DJ on 2003-11-03 17:07:08