A walled yard contains only sparrows and cats, and you may not look inside. Counting over the wall you get 40 eyes and 56 legs. Every animal is intact: no one-legged sparrows, no three-legged cats, and at least one of each species is present. How many cats are in the yard?

**8 cats**, and therefore 12 sparrows.

Eyes and Legs in the Yard

Issue 1 Warm-up Published 6 Aug 2026 By The Chalkboard Desk

The problem

A walled yard contains only sparrows and cats, and you may not look inside. Counting over the wall you get eyes and legs. Every animal is intact: no one-legged sparrows, no three-legged cats, and at least one of each species is present. How many cats are in the yard?

Every sparrow has exactly legs and eyes.
Every cat has exactly legs and eyes.
The yard contains at least one sparrow and at least one cat.

Take a minute

Reveal hint 1

Two eyes per animal is not a coincidence — the eye count alone gives you the total number of animals before you touch the legs.

Reveal hint 2

Once you know the head count, let the number of cats be and write the leg total as a single equation in .

Solution

Answer**8 cats**, and therefore sparrows.

Derivation

Read the head count off the eyes.
Name the unknown.
Write the leg total.
Solve the linear equation.
Verify against both counts.