Two players play with a pile of 2024 chips placed on a table. Each in turn, a player removes a certain number of chips from the gaming table: at least one chip, but no more than half of the chips still on the table. The person who leaves only one chip on the table is declared the loser. Who will win the game, the player who starts or the other one?
I have the feeling that the player who starts can win every time but I can't find the winning strategy. Can you help me to find which player is winning and what is their strategy? Thanks in advance.
if it's your turn and there is
1 chip : victory
2 chips : loss
3 : victory
4 : victory
5 : loss
6 - 10 : victory (make it 5)
11: loss
23: loss
you can realize the loss pattern is 2n + 1, and pretty easy to prove. you can calculate, or think about the fact that 2n + 1 is always odd, so if there is an even amount(2024), the first player wins!