- Without Rahmat
Today Rahmat left the dorm for helping his family till Wednesday. They are going to work in their garden, they have to manage their yield. I wish plague doesn't ruin their crops and have good crops.
Today was a bit boring because we had used to each other and Rahmat and I were good at making fun of Faraz :)
Faraz and I went out and eat ice cream again. Without Rahmat we can't play Rocket League and I have missed it so much.
- Using Symmetry in Game Theory Problems
I have encountered many game theory problems that needs to use Symmetry for solving them.
Today I stuck on one of them : 120E. Put Knight
Problem says that 2 players A and B are playing on a chessboard with size n*n. They take turns to put a Knight on board such that no two Knight threat each other. The player who can't move loses.
Solution : At first glance it seems so hard problem but actually it is so easy if you know how to use symmetry rules!
If n was odd : A can put first knight at center of the board and after that if B can find any place to put his knight then A also has a place to put his next knight , exactly in symmetric place of the B's knight respect to the center that certainly is empty ( also new 2 pieces can't threat each other ), so A is the winner !
If n was even : Divide the board to 2 same parts vertically. Every place that A puts his knight , B can put his knight at exact same row but in symmetric place of A's knight respect to the divider line ( also new 2 pieces can't threat each other ), so B is the winner !