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A group of ten

Source: Indian RMO 1993 Problem 7

October 23, 2005
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Problem Statement

In the group of ten persons, each person is asked to write the sum of the ages of all the other nine persons. Of all ten sums form the nine-element set {82,83,84,85,87,89,90,91,92}\{ 82, 83,84,85,87,89,90,91,92 \}, find the individual ages of the persons, assuming them to be whole numbers.
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