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Squares and rectangles.(DISCOVERY)
Australian Mathematics Teacher
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June 22, 2006|
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COPYRIGHT 2006 The Australian Association of Mathematics Teachers, Inc. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group.
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There are some interesting problems to solve involving squares and rectangles. Here are a few for your students to try.
Problem 1
Latin squares have applications in statistical experimental design and in combinatorics. The idea is to take N sets of consecutive numbers 1 to N and place them in an N x N rectangular array so that no number is repeated in any row, column or main diagonal.
For N = 4 you will need a 4 x 4 square array numbered 1 to 4 (with 4 of each). A solution is shown in Figure 1, but many others are possible.
Your students ...
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