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(6): Lost their marbles (full solution) by DJ)
Wow! DJ... don't take it so personally... And there was nothing presumptuous about it.
If Jack pics a number, of COURSE he started with a square.... Every number is a square :-). (But we already went through that.)
And you simply didn't address the issue of why Ravi would have mentioned a 'perfect' (or an 'even') square only once in the three times he referenced a square. (This is my logic, not what you implied.)
Clearly... there is something different about the third time he referenced a square. You (presumptuously) assumed that the other two times he meant a square as well.... Why?!? Answer: because you presumptuously understood that 'a square' meant a perfect square (as we all did).
Again, the difference of using 'even' in the third reference meant something special. It limited it... not not being 'the lowest' solution otherwise.
But no hard feelings here DJ... And I hope you're right, and Ravi intended even to mean 'integral'.
Cheers!
re(7): Lost their marbles (full solution)
