Problem 19 · 2013 Math Kangaroo
Hard
Counting & Probability
careful-countingcasework
How many different ways are there in the diagram shown to get from point A to point B, if you are only allowed to move in the directions indicated by the arrows?
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Answer: D — 12
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Hint 1 of 2
Count paths by labelling each junction with how many ways reach it from A.
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Hint 2 of 2
Only the indicated arrow directions are allowed, so every move goes forward toward B.
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Approach: count directed paths by accumulating at each node
- Label each junction with the number of allowed paths reaching it from A, starting with 1 at A.
- Add incoming counts along the arrow directions, junction by junction, down to B.
- The total number of paths arriving at B is 12.
Mark:
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