I was recently presented with a problem where I have a 10x10 grid and a marker that starts at position (1, 1). Two players are able to manipulate the marker by moving it as far right, or (exclusive) as far up as they would like once on each of their respective turns. The player to finally move the marker into the space at (10, 10) would be the winner.
How would I develop a strategy such that either player can guarantee victory for themselves. I seem to suspect that the player that moves second has the advantage. Is there a way I can mathematically represent this?
HINT: Show that the second player can always move to a point on the diagonal (i.e., one with both coordinates the same).