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Problem of the Week 818

Integer Averages

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The sequence {1, 3, 2} has the property that the average of the first two entries is an integer, as is the average of the first three entries.

Is there a permutation of the positive integers, a1, a2, a3, . . . , such that the average of each initial segment is an integer?

Source: The most recent issue of Quantum: Sept/October 1996 by A Shapovalov.

© Copyright 1996 Stan Wagon. Reproduced with permission.

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