Tricky ages!
In a group of ten persons, each person is asked to write the sum of the ages of all other nine persons. If all the ten sums form the nine element set , find the individual ages of the persons, assuming them to be whole numbers (of years).
Input your answer as the sum of ages of the ten persons.
The answer is 97.
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1 solution
If we sum all ten age sums, each age will be repeated 9 times. Dividing this sum by 9 gives the sum of all ages of the ten persons. The catch is that if all then sums form a nine element set, two sums have the same value. How do we find the repeated sum? Summing up the given 9 sums, we get 783, which is divisible by 9. Assuming the total with the 10 sums is also divisible by 9 (the years are whole numbers), then the repeated sum should also be divisible by 9. The only sum from the list that is divisible by 9 is 90, so this is the repeated sum. Adding is to 783 we get 873, which divided by 9 is 97, the sum of all ages of the then persons.