Two players, A and B, each have an infinite number of coins. They are sitting around a perfectly round table and playing a game:
- On each turn, a player places exactly one coin on the table.
- A coin must be placed completely on the table without overlapping any coin already placed.
- The player who places the last coin wins the game.
- Player A always makes the first move.
Suggest a strategy that guarantees Player A wins, no matter how Player B plays.
Check if you were right - full answer with solution below.
Step 1: First Move
Player A places the first coin at the exact centre of the circular table.
Step 2: B’s Move
Player B places a coin anywhere on the table where it does not overlap with the existing coin.
Step 3: Mirror Move
Player A follows a mirroring strategy. Whenever Player B places a coin, Player A places another coin at the diametrically opposite position (the point directly across the centre of the table).
- Player A continues following this strategy after every move made by Player B.
- Since the table is perfectly round, the opposite position of any coin is also available if Player B's coin fits.
- The coins placed by Player A do not overlap with the coins already on the table.