• Shanelle and Mannfred play a game by taking turns.
• They constitute a circle with 2023 other people, and on each turn Shanelle or Mannfred can remove one of their neighbors to the left or right from the circle.
• Shanelle will win if she successfully removes Mannfred, but Mannfred will win if he is able to remove Shanelle.
Shanelle starts the game followed by Mannfred. Who has a winning strategy?
There are an odd number of people whether you count Shanelle and Mannfred or not. So between Mannfred and Shanelle, in one direction there are an odd number of people, but on the other side an even number of people. By taking fom the even side the first player can make M and S's separation odd in either direction.
Player 2 is then forced to make one odd and one even again. This continues repeatedly. At some point, player 1 will make each of the separations be 1 person. Player 2 then has to take away one of those, after which player1 can remove player 2.
Player 1, Shanelle, wins.
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Posted by Charlie
on 2023-06-19 09:20:34 |
solution (spoiler)
