A medium question on chickens and rabbits for P3–P4, 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 13 chickens and rabbits, with 28 legs in all.
Each chicken has 2 legs and each rabbit has 4.
How many chickens are there?
Show the hints (2)
💡Hint 1: Suppose all 13 were chickens. How many legs would that be, and how far off is it?
💡Hint 2: How many more legs does each chicken swapped for a rabbit add? How many swaps make up the difference?
Worked solution
Have a go first, then read the solution step by step.
1.Suppose all 13 were chickens: 13 × 2 = 26 legs.
2.But there are really 28: the supposing is 28 − 26 = 2 short.
3.Swap one chicken for a rabbit: still 13 in all, but 4 − 2 = 2 more legs.
4.To make up the 2, swap 2 ÷ 2 = 1 times: there are 1 rabbit.
5.Chickens: 13 − 1 = 12.
⚠️Common mistake: stopping early. Assuming all chickens gives the number of rabbits; take it from 13.
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