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Problem of the Week 1004

Make Them Fit

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Construct a set of ten 2x2 matrices whose entries are integers in the set {1,2,3,4,5}, such that each of the 20 ordered pairs {i,j}, with i not equal to j, appears once as a row, once as a column, and once as a NW-SE or NE-SW diagonal.

Source: Dirk Laurie. This problem arose from an actual problem in setting up a mixed doubles tennis tournament in South Africa.

© Copyright 2004 Stan Wagon. Reproduced with permission.

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2 March 2004