A hard question on tree planting for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P2 to P5 papers. Sawing logs, striking clocks and lining up lamp posts are all the same problem.
The question
Trees line both sides of a straight road: on each side they run from one end to the other, with a tree at each end and neighbouring trees 8 m apart.
There are 32 trees in all.
Both sides are now to be replanted with a tree every 6 m, still with trees at both ends.
An old tree that already stands on a new spot stays; the other old trees are removed, and every new spot without a tree gets a new one.
How many new trees are planted?
Show the hints (3)
💡Hint 1: Look at one side first: how many trees does it have? From that, work out how long the road is.
💡Hint 2: How many trees does one side need under the new plan? Which of those spots already have a tree that can stay?
💡Hint 3: The road is 120 m. Spots that keep their tree come every 24 m, both ends included: 6 per side. The new plan needs 21 per side.
Worked solution
Have a go first, then read the solution step by step.
1.One side has 32 ÷ 2 = 16 trees, so 15 gaps: the road is 15 × 8 = 120 m.
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