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Problem of the Week
Problem E
Twelve Cousins

Arya has twelve cousins. She secretly writes their ages, as positive integers, on a piece of paper. She then tells you the mean (average) of the twelve ages is \(8.75\) and the median is \(10\). Finally, she draws you the following histogram to represent the ages of her cousins.

A histogram of the Ages of Arya’s Cousins with horizontal
axis labelled Ages and vertical axis labelled Frequency. There are 3
people in the age range of 1 to 4, 2 people aged 5 to 8, and 7 people
aged 9 to 12.

How many possibilities are there for the ages of Arya’s twelve cousins?