Bottle Imp Puzzle

Description of Game

The game of Bottle Imp, published by Bambus, is played with a bottle and 37 numbered cards, some red, some blue, and some yellow.

It is usually played by three players.

The bottle, which contains an Imp, starts with card 19; this is the price of the bottle. The other 36 cards are dealt out to the players. Each passes one card to each opponent and to the Imp. After passing, each player has 11 cards.

Eldest hand leads to the first trick. Players must follow suit if they can. A trick is won by the highest card that is lower than the price of the bottle. The winner of such a trick acquires the bottle as well, and the winning card becomes the new price of the bottle. If all cards in a trick exceed the price of the bottle, the highest card wins and the bottle stays put. Suit does not matter in determining which card wins a trick. The winner of a trick leads to the next trick.

Every card except 19 has a scoring value. At the end of the hand, the player with the bottle loses the scoring value of the Imp's three cards. Each other player wins the scoring value of the cards he took in tricks.


At the end of a hand, what is the highest possible price of the bottle? That is, what is the highest card that can win the bottle for the last time?

{ Solution }

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