Some of the oldest puzzles in history involve “figuring out” people’s ages. They are found in ancient texts across cultures, demonstrating a long-standing fascination with imaginative and logical thinking wrapped into one, which is essentially what "figuring out" refers to. They have been a staple in collections of brainteasers since at least the medieval ages, starting with Alcuin’s early ninth-century manuscript, Propositiones ad acuendos juvenes (“Problems to Sharpen Young Minds”), which contains several challenging age problems.

Such puzzles require us to determine the ages of certain people on the basis of given information. The term “figure out” is an apt one, because it encompasses a wide range of mental activities involving the manipulation and coordination of ideas as if they were “figures” to be put together like jigsaw puzzle pieces—hence the blending of imagination and logic.

Here’s a simple example.

Alma, Natasha, and Maria are three young children. Natasha is twice as old as Alma, but half Maria’s age. The sum of their ages is just 14. How old is each one?

The information allows us to establish that Alma is the youngest. If we assign the age of 1 to Alma, then Natasha would be 2 (twice Alma’s age) and Maria would be 4, since Natasha’s age of 2 would be half this age. Adding them up, we get 1 2 4........

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