382 Frequently Asked Questions In Quantitative Finance
Ages of three children
A census taker goes to a house, a woman answers the
door and says she has three children. The census taker
asks their ages and she says that if you multiply their
ages, the result is 36. He says he needs more info so she
tells him that the total of their ages is the address of the
building next door. He goes and looks, then comes back
and says he still needs more information. She tells him
that she won’t answer any more questions because her
eldest child is sleeping upstairs and she doesn’t want to
wake him.
What are the children’s ages?
(Thanks to tristanreid.)
Solution
First suitably factorize 36: (1,1,36), (1,4,9), (1,2,18),
(1,3,12), (1,6,6), (2,3,6), (2,2,9), (3,3,4).
When the census taker is unable to decide from the
information about nextdoor’s house number we know
that nextdoor must be number 13, because both (1,6,6)
and (2,2,9) add up to 13. All of the other combina-
tions give distinct sums. Finally the mother refers to
the ‘eldest child,’ and this rules out (1,6,6) because the
two older children have the same age. Conclusion the
ages must be two, two and nine.
Caveat: (1,6,6) is technically still possible because one
of the six-year olds could be nearing seven while the
other has only just turned six.
Ants on a circle
You have a circle with a number of ants scattered
around it at distinct points. Each ant starts walking
