A hard question on chickens and rabbits for P4–P5, with a step-by-step solution, diagrams and the answer. One of the best-known Olympiad problem types: in the Hua Xia Cup it appears from the P2 first round to the P5 papers.
The question
In a cage on a farm there are 64 chickens and rabbits.
Each chicken has 2 legs and each rabbit has 4.
The chickens have 56 more legs than the rabbits.
How many rabbits are there?
Show the hints (3)
💡Hint 1: Suppose all 64 were chickens. How many more legs would the chickens have than the rabbits?
💡Hint 2: Each chicken swapped for a rabbit: the chickens lose 2 legs and the rabbits gain 4. How much does the gap shrink?
💡Hint 3: From 128 more down to 56 more is a drop of 72, at 6 a swap.
Worked solution
Have a go first, then read the solution step by step.
1.Suppose all 64 were chickens: 64 × 2 = 128 chicken legs against 0 rabbit legs, so 128 more.
2.Each chicken swapped for a rabbit: the chickens lose 2 legs and the rabbits gain 4, so the gap shrinks by 2 + 4 = 6.
3.In fact the chickens are 56 ahead. The gap fell from 128 to 56: 128 − 56 = 72.
4.At 6 a swap, that is 72 ÷ 6 = 12 swaps: 12 rabbits.
5.Check: 52 × 2 = 104, 12 × 4 = 48, 56 apart ✓
⚠️Common mistake: thinking each swap changes the gap by 4 − 2 = 2. One side loses 2 and the other gains 4, so the gap moves by 6.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download