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The Farmyard Legs Brain Teaser
A farmyard has only chickens and cows in it. The farmer counts 20 heads and 56 legs altogether. How many cows are there?
Show the worked solution
What's the puzzle?
A farmyard has only chickens and cows in it. The farmer counts 20 heads and 56 legs altogether. How many cows are there?
What's the answer?
8 cows (and 12 chickens)
How do you work it out?
- Every animal has one head, so there are 20 animals.
- If all 20 were chickens, there would be 20 × 2 = 40 legs.
- There are 56 legs, so 56 - 40 = 16 legs are unaccounted for. Each cow has 2 more legs than a chicken.
- 16 ÷ 2 = 8, so 8 of the animals are cows.
- There are 8 cows and 12 chickens. Check: 8 × 4 + 12 × 2 = 32 + 24 = 56 legs.
Frequently asked questions
Can the farmyard legs puzzle be solved without algebra?
Yes. The farmyard legs puzzle can be solved by assuming every animal is a chicken, counting the legs that would give, and sharing the extra legs out as cows. This makes it a good puzzle for KS2 students who have not met equations yet.
How would an older student solve the farmyard legs puzzle?
An older student could solve the farmyard legs puzzle with simultaneous equations: c + h = 20 and 4c + 2h = 56. LoveMaths Tutoring UK uses this puzzle to show that the same problem can be cracked with reasoning at KS2 and with algebra later on.
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