Imagine a 24-by-24 chessboard. Now suppose you started counting all of the "sub-squares" on that board, squares of lengths 1 through 24 found by tracing the sides of the squares of the big board. To remind you how many sub-squares you've counted, you make a pile of little squares of all equal size (which you just happen to have lying around), one little square for each sub-square.
It turns out that these little squares can be put together, edge to edge, to form an even bigger chessboard.
What is the length of each side of the giant chessboard?
(In reply to answer
by K Sengupta)
It can be established that, in general for mxm square boards, the total number of sub squares
= Sum of squares of all natural numbers uptill m
In the given problem, m=24.
Thus, the required total number of sub squares
Thus, the length of each side of the giant chessboard