Problem 9 · 2019 Math Kangaroo
Medium
Counting & Probability
grid-countingcareful-counting
The picture shows a mouse and a piece of cheese. The mouse is only allowed to move to the neighbouring fields in the direction of the arrows. How many paths are there from the mouse to the cheese?
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Answer: E — 6
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Hint 1 of 2
The arrows only let the mouse go forward toward the cheese, never back.
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Hint 2 of 2
Trace one path with your finger, then carefully find every different way without repeating one.
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Approach: trace every allowed path one at a time and count them
- Put your finger on the mouse and follow the arrows toward the cheese.
- Each time you reach a spot with two arrows, you can pick a different way to go.
- Carefully trace each different route all the way to the cheese without repeating one.
- Counting all the different routes gives 6, so the answer is E.
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