Square Deal (Posted on 2003-06-30)

	Submitted by DJ
Rating: 3.8182 (11 votes)
Solution:	(Hide)
70 To find the number of squares on a 24-by-24 chessboard, first consider the 3-by-3 case. In that case, there are three 1-by-1 squares, 4 2-by-2 squares, one containing each corner, and of course the entire 3-by-3 square, for a total of 9+4+1=14 sub-squares. In general, the number of sub-squares on an n-by-n chessboard is the sum of all the square numbers less than or equal to n². This summation is: 1²+2²+...+(n-1)²+n² =Σ[i=1→n](i²) This is equal to: n(n+1)(2n+1)/6 For n=24, the number of sub-squares is 24(25)(49)/6=4900. This is equal to 70², so there are 70 squares on each side of the larger chessboard you created.

	Subject	Author	Date
	Problem Solution With Explanation	K Sengupta	2007-05-15 15:11:48
	answer	K Sengupta	2007-05-15 15:05:48
	Unique chessboard	Nick Hobson	2004-08-26 16:32:03
	Solution	Lawrence	2003-08-27 02:01:54
	re: Difficulty change	DJ	2003-07-07 06:28:20
	My solution	Hank	2003-06-30 04:45:08
	solution	Charlie	2003-06-30 03:20:17
	Difficulty change	Gamer	2003-06-30 02:47:45
	No Subject	Matt	2003-06-30 02:20:42