Question 4
There is a row of $100N$ ham sandwiches. In one action a boy eats the first sandwich from either end; in one action his cat either eats the ham from one remaining sandwich or does nothing. The boy performs 100 actions per turn, the cat one action per turn, and they alternate, with the boy starting. The boy wins if the last sandwich he eats contains ham. Can he guarantee a win for every positive integer $N$, regardless of the cat's play? (8 points)
Neutral editorial illustration.
Neutral editorial illustration.