Problem 10 · 2018 Math Kangaroo
Hard
Counting & Probability
path-tracingcareful-counting
In the diagram shown you follow the arrows to get from A to B. How many different ways are there that do this?
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Answer: B — 16
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Hint 1 of 2
Every route from A must pass through the single centre node before reaching B.
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Hint 2 of 2
Count the ways from A to the centre, count the ways from the centre to B, then multiply.
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Approach: multiply the routes into the centre by the routes out of it
- All arrows from A funnel into the central node, and all arrows out of the centre lead toward B.
- From A to the centre there are 4 routes; by the diagram's symmetry there are also 4 routes from the centre to B.
- So the number of full routes is \(4\times 4 = \) 16.
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