2024 Mock AMC 10 - Problem 6

Ivan and Owen are playing a game, where the goal is to move a cart from the top-left cell to the bottom-right cell of an 80 \times 80 board without moving the cart out of the board. Without changing columns, Ivan can move the cart down 1, 2, or 3 rows. Owen can move the cart right 1, 2, or 3 columns without changing rows. If a player can't move, they lose. Given that Ivan moves first and both play optimally, find the minimum number of moves that Ivan can make to guarantee his win.

\textbf{(A) }39\qquad\textbf{(B) }40\qquad\textbf{(C) }77\qquad\textbf{(D) }78\qquad\textbf{(E) }\text{It is impossible for Ivan to win the game.}