Puzzle | Round table coin game

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.

👁 coin_1

Step 2: B’s Move

Player 2 places a coin anywhere on the table (e.g., near the boundary).

👁 coin_2

Step 3: Mirror Move

Player 1 responds by placing a coin at the diametrically opposite position, maintaining equal distance from the boundary.

👁 coin_3

• 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.