Competition problem — Combinatorics

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Combinatorics Difficulty 4.2 AIME Find the answer United States

Problem:

After walking so much that his feet get really tired, the beaver staggers so that, at each step, his coordinates change by either $(+1,+1)$ or $(+1,-1)$ . Now he walks from $(0,0)$ to $(8,0)$ without ever going below the $x$ -axis. How many such paths are there?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution: $C(4)=14$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.