Difference between revisions of "2014 UNCO Math Contest II Problems/Problem 1"
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== Problem == | == Problem == | ||
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| + | The Duchess had a child on May 1st every two years until she had five children. This year the | ||
| + | youngest is <math>1</math> and the ages of the children are <math>1, 3, 5, 7</math>, and <math>9</math>. Alice notices that the sum of the ages | ||
| + | is a perfect square: <math>1 + 3 + 5 + 7 + 9 = 25</math>. 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? | ||
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== Solution == | == Solution == | ||
Revision as of 15:42, 19 October 2014
Problem
The Duchess had a child on May 1st every two years until she had five children. This year the
youngest is 
and the ages of the children are 
, and 
. Alice notices that the sum of the ages
is a perfect square: 
. 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?
