Problem 16 · 2010 Math Kangaroo
Medium
Counting & Probability
careful-countingcasework
In the diagram one should go from A to B along the arrows. Along the way, add up the numbers that are stepped on. How many different results can be obtained?
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Answer: B — 2
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Hint 1 of 2
List the possible routes from A to B that follow the arrows.
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Hint 2 of 2
Add the circled numbers on each route and see how many different totals appear.
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Approach: enumerate the arrow routes
- Follow every allowed path from A to B and total the numbers stepped on.
- The different routes give only a couple of distinct sums.
- The number of different results is 2.
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