In the first pile there are 100 sweets and in the second there are 200. Consider the game with two players where: in one turn a player can take any amount of sweets from one of the piles. The winner is the one who takes the last sweet. Which player would win by using the correct strategy?
a) The vertices (corners) in a regular polygon with 10 sides are colored black and white in an alternating fashion (i.e. one vertex is black, the next is white, etc). Two people play the following game. Each player in turn draws a line connecting two vertices of the same color. These lines must not have common vertices (i.e. must not begin or end on the same dot as another line) with the lines already drawn. The winner of the game is the player who made the final move. Which player, the first or the second, would win if the right strategy is used?
b) The same problem, but for a regular polygon with 12 sides.