A medium question on clever sums for P2–P4, with a step-by-step solution, diagrams and the answer. The first few questions of a competition paper are often clever sums, and the Hua Xia Cup has them in every year from P1 to P6.
The question
Can you work this out fast, without adding one by one?
9 + 10 + 11 + … + 23 + 24 = ?
What is the answer?
Show the hints (2)
💡Hint 1: Pair the ends: 9 + 24, 10 + 23, … What is each pair?
💡Hint 2: How many numbers from 9 to 24? So how many pairs?
Worked solution
Have a go first, then read the solution step by step.
1.From 9 to 24 there are 24 − 9 + 1 = 16 numbers: 16 ÷ 2 = 8 pairs.
2.Pair the ends: each pair is 9 + 24 = 33: 33 × 8 = 264.
⚠️Common mistake: thinking there are 24 − 9 = 15 numbers. 24 − 9 = 15 is the number of steps from 9 to 24; there is one more number than steps.
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