2002 Gauss 8 Problem 25

Emily has created a jumping game using a straight row of floor tiles that she has numbered 1, 2, 3, 4, \ldots . Starting on tile 2, she jumps along the row, landing on every second tile, and stops on the second last tile in the row. Starting from this tile, she turns and jumps back toward the start, this time landing on every third tile. She stops on tile 1. Finally, she turns again and jumps along the row, landing on every fifth tile. This time, she again stops on the second last tile. The number of tiles in the row could be

\textbf{(A)}\ 39\quad \textbf{(B)}\ 40\quad \textbf{(C)}\ 47\quad \textbf{(D)}\ 49\quad \textbf{(E)}\ 53

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.