Chomp 2

After winning the previous game, your friend is back for revenge. This time, he has a chocolate bar made of $n$n by $n$n squares. The same rules apply:

• You will take turns picking a square of chocolate to eat, then eating all the squares to the top, the right, and top-right of the chosen square.
• You must eat at least one square on your turn, and you cannot skip your turn.
• Whoever eats the mouldy square loses.

Should you go first or second? And how will you ensure that you don’t eat the mouldy square?

Solution

Choose to go first, eating the square to the top-right of the mouldy square. This leaves the chocolate bar with the following shape:

On your friend’s turn, he’ll be able to remove squares from either the horizontal or vertical line, but not both. If he removes squares from one of the lines, you remove the same number of squares from the other line. This way, you’ll always be able to force him to eat the mouldy square.