Competition problem — Combinatorics

Library / /18 of 48

Combinatorics Difficulty 4.2 AIME Find the answer United States

Problem:

A beaver walks from $(0,0)$ to $(4,4)$ in the plane, walking one unit in the positive $x$ direction or one unit in the positive $y$ direction at each step. Moreover, he never goes to a point $(x, y)$ with $y>x$ . How many different paths can he walk?

Your answer

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

Solution

Solution:

$C(4)=14$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

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