Problem 20 · 2022 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracing
A road leads away from each of the six houses (see diagram), but the hexagon of roads for the middle is missing. Which hexagons can go in the middle so that you can travel from A to B and to E, but not to D?
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Answer: C — 1 and 5
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Hint 1 of 3
The roads inside the hexagon decide which houses get joined to which — put your finger on A and see where you can drive.
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Hint 2 of 3
You want A, B and E all on one set of connected roads, but D left out with no way to reach it.
Still stuck? Show hint 3 →
Hint 3 of 3
Try each hexagon in the gap and trace the roads from A every time.
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Approach: drop in each hexagon and trace the roads from A
- Fit a hexagon into the gap, then put your finger on house A and follow every road you can drive along.
- You need A, B and E to all join up, while D stays cut off (no road reaches it).
- Only hexagons 1 and 5 connect A to B and E while leaving D alone.
- So the answer is 1 and 5 (choice C).
Mark:
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