Problem 19 · 2022 Math Kangaroo
Hard
Geometry & Measurement
careful-counting
There are three paths running through our park in the city (see diagram). A tree is situated in the centre of the park. What is the minimum number of trees that have to be planted additionally so that there are the same number of trees on either side of each path?
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Answer: C — 3
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Hint 1 of 2
Each path must split the trees evenly, so it needs an equal count on both sides.
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Hint 2 of 2
Add trees so that every one of the three paths is balanced at once.
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Approach: balance the tree count across all three dividing paths
- Each path divides the park into two parts that must hold equally many trees.
- Place extra trees so that all three balance conditions hold at once, including the existing central tree.
- The minimum number of additional trees needed is 3.
Mark:
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