Thirteen animals, forty-four legs, and no way to start counting. Heads alone allow any split; legs alone allow any split. Only together do they fix one field — which is why this is a puzzle rather than a sum.
The method is worth more than the answer, and it needs no algebra. Assume every animal is a chicken: thirteen animals would then have twenty-six legs. There are eighteen more than that. Every chicken swapped for a rabbit adds exactly two legs, so eighteen divided by two is nine rabbits. A child who can double and halve can run it.
Why this sheet works
Two wrong first moves are almost universal, and both are worth letting happen: halving the legs, and halving the animals. Neither gives the answer, and seeing why is most of the learning. The answer key prints the full route so the conversation afterwards has something to point at.
Find how many four-legged animals. Show how you worked it out.
1A field holds 20 chickens and rabbits altogether. Between them they have 50 legs.How many are rabbits?Why
2A farmyard has 18 ducks and sheep in it. Counting every leg comes to 48.How many are sheep?Why
Chickens and rabbitsUp to 60 animals
Name: Date:
Find how many four-legged animals. Show how you worked it out.
3A pet shop keeps 51 parrots and cats. Altogether they stand on 188 legs.How many are cats?Why
435 flamingos and zebras are drinking at a waterhole. There are 86 legs in the water and on the bank.How many are zebras?Why
Chickens and rabbits · Up to 60 animalsAnswer key
1. If all 20 had two legs there would be 40 legs. There are 50, which is 10 more. Swapping a two-legged one for a four-legged one adds 2 legs, so 10 ÷ 2 = 5 rabbits. More than one way works here. The other is to write both facts down and take one from the other: the two counts add to 20, and twice the first plus four times the second is 50. Doubling the first fact gives 40, and 50 − 40 = 10 left over — two extra legs for each of the 5 rabbits.2. If all 18 had two legs there would be 36 legs. There are 48, which is 12 more. Swapping a two-legged one for a four-legged one adds 2 legs, so 12 ÷ 2 = 6 sheep. More than one way works here. The other is to write both facts down and take one from the other: the two counts add to 18, and twice the first plus four times the second is 48. Doubling the first fact gives 36, and 48 − 36 = 12 left over — two extra legs for each of the 6 sheep.3. If all 51 had two legs there would be 102 legs. There are 188, which is 86 more. Swapping a two-legged one for a four-legged one adds 2 legs, so 86 ÷ 2 = 43 cats. More than one way works here. The other is to write both facts down and take one from the other: the two counts add to 51, and twice the first plus four times the second is 188. Doubling the first fact gives 102, and 188 − 102 = 86 left over — two extra legs for each of the 43 cats.4. If all 35 had two legs there would be 70 legs. There are 86, which is 16 more. Swapping a two-legged one for a four-legged one adds 2 legs, so 16 ÷ 2 = 8 zebras. More than one way works here. The other is to write both facts down and take one from the other: the two counts add to 35, and twice the first plus four times the second is 86. Doubling the first fact gives 70, and 86 − 70 = 16 left over — two extra legs for each of the 8 zebras.
