AMO · 2027 · Grades 6-7 · Self-study SET 31 Question 13

An M-shaped MOEMS tile is made from a 5 by 5 square by removing two 4 by 1 rectangles, as shown. Jimmy wants to place as many tiles as possible on a 6 by 42 game board without overlap. What is the maximum number of tiles? Tiles must lie entirely on the board and may be rotated or flipped.



**Input:** Enter the integer only, without units.