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Coins on Round Table Puzzle
Solve the Coins on Round Table Puzzle
A detailed solution for coins on Round Table Puzzle is given here.
Two players (Player A & Player B) are playing a game on a circular table of finite diameter.
The game is to take turns and place a coin on the table. The coin should always be put down on the surface & can’t be stacked on top of one another. A limited amount of coins can be put on the table. The player who puts the last coin on the surface wins.
Objective
Suggest a strategy for Player A, so that no matter what Player B does, he will always win.
Assumption
Player A will always make the first move
Solve the Coins on Round Table Puzzle
A detailed solution for coins on Round Table Puzzle is given here.
Two players (Player A & Player B) are playing a game on a circular table of finite diameter.
The game is to take turns and place a coin on the table. The coin should always be put down on the surface & can’t be stacked on top of one another. A limited amount of coins can be put on the table. The player who puts the last coin on the surface wins.
- Objective
Suggest a strategy for Player A, so that no matter what Player B does, he will always win.
- Assumption
Player A will always make the first move
Solution
Step 1:-
- Player 1 must, place the coin in the centre of the table.
Step 2:-
- Wherever Player 2 keeps their coin, place the coin on the opposite side, at the same distance from boundary
Step 3:-
- This will keep on happening
- If player 2 has space to keep the coin on the table
- Then player 1 will also have space to keep the coin
- As he has been placing his coin always diagonally opposite
This player 2 will run out of space first.
Inference:-
- For whichever position the second player uses, the first player will be able to put their coin opposite to it.
- Since the table is finite, at some point the second player will run out of space to put their coin.
- The first player will not run out of space, as their position is always opposite to that of the other player. Hence as long as the second player has a slot to put their coin the first player will automatically get the slot opposite to it empty.
- By playing like this, the first player will eventually win, when the second player runs out of free slots.
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