A hard question on clever sums for P4–P5, 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
Work this out the clever way.
4 + 7 + 10 + … + 22 + 25 = ?
What is the answer?
Show the hints (3)
💡Hint 1: How much bigger is each number than the one before? How many numbers from 4 to 25?
💡Hint 2: Going from 4 to 25 in steps of 3, how many steps? There is one more number than steps.
💡Hint 3: There are 8 numbers, and each end-pair adds to 29.
Worked solution
Have a go first, then read the solution step by step.
1.Going up 3 at a time, 4 to 25 takes (25 − 4) ÷ 3 = 7 steps; there is one more number than steps: 7 + 1 = 8 numbers.
2.Pair the ends: each pair is 4 + 25 = 29.
3.Write the numbers in a row, and again backwards under it: every column makes 29, there are 8 columns, and the two rows are twice the sum: sum = 29 × 8 ÷ 2 = 116.
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