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Riddle of the Week #34: Two Wizards Ride a Bus

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This week we take a look at a notoriously tricky math puzzle, one originally penned by English mathematician John Conway back in the 1960s. Apparently he was riding the bus home one evening when he encountered a pair of wizards.

Last night I sat behind two wizards on a bus and overheard the following:

Blue Wizard: I have a positive integer number of children, whose ages are positive integers. The sum of their ages is the number of this bus, while the product is my own age.

Red Wizard: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?

Blue Wizard: No, you could not.

Red Wizard: Aha! At last, I know how old you are!

Apparently the Red Wizard had been trying to determine the Blue Wizard’s age for some time. Now, what was the number of the bus?

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