2024 Mock AMC 10 - Problem 19

An ant is placed randomly in a 50 \times 20 rectangle. It then walks n units north, south, east, or west (chosen at random with a \frac{1}{4} chance for each direction) once, and then stops. Find the minimum positive integer value of n, such that the probability that the ant leaves the rectangle is greater than \frac{1}{2}.

\textbf{(A) }11\qquad\textbf{(B) }12\qquad\textbf{(C) }14\qquad\textbf{(D) }15\qquad\textbf{(E) }18