Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

Question

07-06-2022
Mathematics

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Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-06-20T15:44:22-04:00

The values of n that either player has a winning strategy is when the number of points are odd such as 3:-

How to depict the strategy?

The game is begun by A and then its chance of B to play the game alternatively, then all the possible moves are 1,2; 2,3; 1,3 in which all possible pairs are selected.

If the game end on an even number of moves then the game is won by A. For B to win, these points should be connected at the very end of the game.

Similarly, for even number of moves B wins the game when number of points is odd.

If the number of points is even the opposite of this happens that is, for even moves B wins and for odd number of moves A wins.

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How to depict the strategy?

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