
Re: Word Problem help
Posted:
Sep 23, 2003 1:18 AM


It all boils down to whether a given number has an odd or even number of distinct factors.
Consider, for example, the number 24. Pair off its factors, x and y, where xy = 24, one always is larger than the other:
1, 24 2, 12 3, 8 4, 6
Since 24 has an even number of factors, the person in seat 24 will return to the original seated postion.
Most numbers have all their distinct factors pairing off in this way, larger and smaller. The numbers which don't are perfect squares. Consider, for example, 36.
1 36 2 18 3 12 4 9 6 6
Note the repeating 6, the principal square root of 36, which is the essence of being a perfect square. Numbers with an odd number of distinct factors are perfect squares. Those will be left standing.
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