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
96−64=32
32÷2=16
- Two numbers, and one of them counts something you cannot see directly: 32 animals altogether, standing on 96 legs.
- 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.
- 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.
- 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.
- 01
Two numbers, and one of them counts something you cannot see directly: 32 animals altogether, standing on 96 legs.
- 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.
- 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.
- 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.