Box of Secrecy
A group of girls (at least two) wanted to know the average age of the entire group but none of them are willing to divulge their age. They devised a strategy by using a calculator that doesn't store steps such that each girl tapped some keys and passed it on to the other girls. After some finite time, they had the average of their ages but no one knows the exact age of any other girls.
If the total number of girls is 99, how many possible number of girls are there such that they can accomplish this task?
Saw this somewhere on the interwebs.
The answer is 97.
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1 solution
If there are only two girls, then from the average either girl can calculate the age of the other, so the goal is impossible.
If there are more than two girls, they can find their average age without giving away any individual ages via the following method:
Thus, the girls can find their average age without giving away their individual ages if and only if there are more than two girls. Since we are assuming there are 99 girls, the answer is 9 7 .