Question 15
An IMSO robot stands on the middle cell of a $1\times19$ board, as shown in the diagram below. It is programmed to make 5 moves. The directions of the moves alternate between left and right (the first move can be in either direction). For each move, the robot will move 1, 2, 3, 4 or 5 cells from its position; the robot should not move out of the board; moreover each number can be used exactly once. How many cells are there on this board on which the robot cannot end up after 5 moves?
