Problem:
Sofiya and Marquis play a game by taking turns. They form a circle with other people, and on each turn Sofiya or Marquis can remove one of their neighbors to the left or to the right from the circle. The person who removes the other player wins. If Sofiya starts, who has the winning strategy?
Solution:
Note that there are an odd number of people in the circle beside Sofiya and Marquis, so Sofiya and Marquis divide the circle into two arcs, one with an even number of people and the other with an odd number of people. Sofiya's winning strategy will be to always remove a neighbor from the even side. This would leave Marquis with an odd number of people on either side of him (excluding Sofiya), so continuing this process would also leave Sofiya with an even side to remove a neighbor from. This process always leaves an odd number of people between Marquis and Sofiya whenever it is Marquis' turn, so he will never be able to remove Sofiya from the circle. This secures Sofiya's win.