Problem 12 · 2022 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracing
There are 5 trees and 3 paths in a park, shown on the map. One more tree is planted so that every path has an equal number of trees on each side of it. In which section of the park is the new tree planted?
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Answer: B — B
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Hint 1 of 2
Each path must split the trees so equal numbers sit on each side; count trees per side of every path now.
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Hint 2 of 2
The new tree must fix every path's balance at once; find the single section on the correct side of all three paths.
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Approach: balance every path at once
- Right now each of the three paths has an unequal split of the five trees.
- Adding one tree must even out all three paths simultaneously.
- The only section that sits on the short side of every unbalanced path is B, so the answer is B.
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