Problem 10 · 2016 Math Kangaroo
Medium
Counting & Probability
careful-counting
A mouse wants to escape a labyrinth (see picture). On her way out she is only allowed to go through each opening once at most. How many different ways can the mouse choose to get outside?
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Answer: D — 6
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Hint 1 of 2
Trace each route from the mouse to the outside, never reusing an opening.
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Hint 2 of 2
Count the separate paths one by one and don't repeat any.
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Approach: trace and count the distinct escape routes
- Start at the mouse and follow the openings outward, using each opening at most once.
- List every different route that reaches the outside.
- Counting them carefully gives 6 routes.
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