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2014 UNCO Math Contest II Problems/Problem 1

Revision as of 14:42, 19 October 2014 by Timneh (talk | contribs)

Problem

The Duchess had a child on May 1st every two years until she had five children. This year the youngest is $1$ and the ages of the children are $1, 3, 5, 7$, and $9$. Alice notices that the sum of the ages is a perfect square: $1 + 3 + 5 + 7 + 9 = 25$. How old will the youngest be the next time the sum of the ages of the five children is a perfect square, and what is that perfect square?


Solution

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