Problem 14 · 2022 Math Kangaroo
Hard
Counting & Probability
path-tracingcareful-counting
A bee called Maja wants to hike from honeycomb X to honeycomb Y. She can only move from one honeycomb to the neighbouring honeycomb if they share an edge. How many different ways are there for Maja to go from X to Y if she has to step onto every one of the seven honeycombs exactly once?
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Answer: D — 5
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Hint 1 of 2
You need a path from X to Y that visits all seven honeycombs exactly once.
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Hint 2 of 2
Work outward from X, pruning routes that strand a cell you can never return to.
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Approach: count the full paths through the seven-cell honeycomb graph
- Model the honeycombs as nodes with edges between cells that share a side.
- Trace every route from X that uses all seven cells exactly once and ends at Y, discarding ones that get stuck.
- Exactly 5 such complete routes exist.
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