Problem 11 · 2025 Math Kangaroo
Medium
Counting & Probability
grid-countingcareful-counting
A mouse wants to reach a piece of cheese. From each square it can only move to the square to its right or to the square directly below it. How many different paths lead the mouse to a piece of cheese?
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Answer: C — 8
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Hint 1 of 2
Instead of drawing every route, write a number in each square: how many ways the mouse can reach that square.
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Hint 2 of 2
A square's number is the sum of the numbers in the square just left of it and the square just above it, since those are the only ways in.
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Approach: fill in path counts square by square
- Write 1 in the start square; every other square gets the total of the square to its left and the square above it (the only squares that can flow into it).
- Filling the staircase this way, the counts grow 1, then 2 and 3, and so on down toward the cheese.
- The cheese squares collect a total of 8 paths, which is (C).
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