Solution to Bottle Imp Puzzle

The bottle starts with a price of 19. Of the 18 cards 1–18, at least 15 must be held by the players. They must be played to at least 5 tricks, so at least one trick must be won by a 14 or lower. Therefore the highest possible losing card is at most 14.

It is not enough to play the 15 low cards on 5 tricks. The players must follow suit when they can. Also, the winner of each trick leads to the next. Fortunately, the winning card need not be in the suit led.

Here is a game in which the losing card is 14. After the pass, player 1 holds:

Player 2 holds:

Player 3 holds:

The starting price of the bottle is 19. Player 1 leads to the first trick:

Player 1 wins with the 18 and leads to the second trick:

Player 2 wins with the 17 and leads to the third trick:

Player 1 has no red cards and plays the 4. Player 3 wins with the 16 and leads to the fourth trick:

Player 2 wins with the 15 and leads to the fifth trick:

Player 3 has no more yellow cards and plays the 14, which wins the trick. Now all cards that remain to be played have values above 14, so Player 3 retains the bottle with a price of 14.

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