Chickens & rabbits, step by step

Thirteen animals, forty-four legs, and no way to start counting.

The question

How many are sheep?

Assume they are all the same, then fix it

animals:32· legs:96
32×2=64
9664=32
32÷2=16
  1. Two numbers, and one of them counts something you cannot see directly: 32 animals altogether, standing on 96 legs.
  2. Pretend every one of them has two legs. That is certainly wrong, and it is easy: 32 × 2 = 64 legs. Starting from something wrong on purpose is the whole trick here.
  3. The real count is 96, so the pretend one is short by 96 − 64 = 32 legs. Those missing legs have to come from somewhere, and there is only one place.
  4. Turning one two-legged animal into a four-legged one adds exactly 2 legs, never more or less. So the number to turn is 32 ÷ 2 = 16 sheep.

How it works.

  1. 01

    Two numbers, and one of them counts something you cannot see directly: 32 animals altogether, standing on 96 legs.

  2. 02

    Pretend every one of them has two legs. That is certainly wrong, and it is easy: 32 × 2 = 64 legs. Starting from something wrong on purpose is the whole trick here.

  3. 03

    The real count is 96, so the pretend one is short by 96 − 64 = 32 legs. Those missing legs have to come from somewhere, and there is only one place.

  4. 04

    Turning one two-legged animal into a four-legged one adds exactly 2 legs, never more or less. So the number to turn is 32 ÷ 2 = 16 sheep.