Two players, A and B, each have an infinite number of coins. They are sitting near a perfectly round table and play the following game:
- On each turn, a player places exactly one coin on the table.
- A coin must be placed on the surface of the table, and cannot overlap any coin already placed.
- The player who places the last coin on the table wins.
- Player A always makes the first move.
Suggest a strategy such that player A will always win, no matter how player B will play
Check if you were right - full answer with solution below.
Step 1: First Move
Player 1 places the first coin at the centre of the table.
Step 2: B’s Move
Player 2 places a coin anywhere on the table (e.g., near the boundary).
Step 3: Mirror Move
Player 1 responds by placing a coin at the diametrically opposite position, maintaining equal distance from the boundary.
- Player 1 keeps mirroring every move of Player 2.
- If Player 2 can place a coin, Player 1 will always have a corresponding spot.
- Therefore, Player 2 runs out of space first, and Player 1 wins.