Rectangles on a Chessboard
Date: 02/09/2002 at 11:10:26 From: Dave Subject: Number of rectangles on a chessboard Dear Dr Maths, How many rectangles are there on a chessboard?
Date: 02/10/2002 at 00:53:06 From: Doctor Schwa Subject: Re: Number of rectangles on a chessboard Hi Dave, Here's a hint on this question that will reveal a beautiful pattern: start in the top left square of the chessboard, and write in each square the number of rectangles whose BOTTOM RIGHT corner is at the bottom right corner of that square. So in the first square you'll write 1 and in the second square you'll write 2 (because there are a 1x1 and 1x2 rectangle that will both have their bottom right corner there) ... Give that method a try, and see how it goes. If you get stuck, there are two other methods of solving this problem in the Dr. Math archives, at Number of Squares in an NxN Square http://mathforum.org/dr.math/problems/fengh.7.29.96.html and a slightly different version of those same two methods is at Squares, Rectangles on a Chessboard http://mathforum.org/dr.math/problems/taur8.14.97.html - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.