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Source: 2024 AMC 8 Problem 13

January 25, 2024
AMCAMC 82024 AMC 8

Problem Statement

Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of 66 hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)
<spanclass=latexbold>(A)</span>4<spanclass=latexbold>(B)</span>5<spanclass=latexbold>(C)</span>6<spanclass=latexbold>(D)</span>8<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>5\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>12