Consider the following game between two players:
• There is an initially rectangular grid of cookies.
• The cookie in the upper left corner is poisoned.
• The players take turns. On a player’s turn, he or she must eat some cookie, along with every cookie to the right and/or below it. (See the diagram for a sample legal move.)
• The losing player is the one who is forced to eat the poisoned cookie. 2
Prove that the player who goes first can always win.
Here is my proof
By the way of contradiction assume the player who goes first does not always win. Lets say the first player eats the lower right cookie in the first try(i.e 4,5). Then in the next turn second player takes turn and ets the cookie at place (3,4). In third round, first player eats the cookie at place (2,3). Then second player eats cookie at place (1,2). Then the first player takes turns and lands on (1,1). SO he loses. So this is contradiction because the second player can force a win. Thus statement is always true.
Can someone please help me on this. Thanks in advance