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
An inter-school maths contest has 22 questions.
Each right answer scores 4 points, each wrong answer loses 3, and a question left blank scores nothing either way.
Ka-ming left 1 blank, answered all the rest, and scored 21.
How many did Ka-ming get right?
Show the hints (3)
💡Hint 1: How many questions did Ka-ming answer?
💡Hint 2: Suppose every answered question were right. What would he score? How much does one wrong answer cost compared with a right one?
💡Hint 3: Each wrong answer is 7 points down on a right one. How many right answers must turn wrong to take away the extra points? That is the number wrong; take it from the number answered.
Worked solution
Have a go first, then read the solution step by step.
1.Ka-ming answered 22 − 1 = 21.
2.Suppose all 21 answered were right: 21 × 4 = 84 points.
3.But he really scored 21: the supposing is 84 − 21 = 63 too many.
4.Turn one right answer into a wrong one: he loses its 4 points and 3 more, 4 + 3 = 7 down.
5.To come down 63, turn 63 ÷ 7 = 9: he got 9 wrong.
6.Right: 21 − 9 = 12.
7.Check: 12 × 4 − 9 × 3 = 21 ✓
⚠️Common mistake: thinking a wrong answer costs only 3, or using all 22 questions and forgetting the one left blank.
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