### Brain Teasers

# Snapoker Championships

The card game Snapoker is a very complex game for four players, requiring the use of two decks of cards with all odd spades, even hearts, prime diamonds (including aces) and non-prime clubs (including aces) removed. Note that jacks are 11, queens are 12, kings are 13. Two jokers are added to the deck and are each worth 15. The cards are dealt among the four players. A hand starts when the dealer shouts "Let's Snapoker!" Following a frenetic minute of randomly throwing all cards onto the table, and at the dealer's call of "Heeeeeeere, piggy, piggy, piggy!" players are required to grab as many cards as they can. Once all cards have been grabbed, the total value of the cards in each player's hand is added up. Points (4, 3, 2 and 1) are awarded to players on each hand, with the highest card total receiving maximum points. In the event of a tie, the player who can drink a glass of milk through their nose the quickest will receive the greater points. A running score is kept throughout the game. The game is over when someone reaches a total of 518 points or when a fight breaks out, which is a common occurrence.

At the 2002 International Snapoker Championships, the final was very hotly contested. Despite the high level of competitiveness in the final, no fights broke out. It was also a day for the history books as it had often been speculated in "Here Piggy!", the official Snapoker magazine, that the longest official Snapoker game, which was played in 1979 and lasted for 186 hands, would never be surpassed (incidentally, this 186-hand game was concluded when the fourth placed player lost his marbles and started the biggest Snapoker fight ever seen). Not only did the 2002 ISC final surpass the 186-hand record, it guaranteed that this new record could never be beaten again, only equalled. How many hands were played in the 2002 ISC final?

At the 2002 International Snapoker Championships, the final was very hotly contested. Despite the high level of competitiveness in the final, no fights broke out. It was also a day for the history books as it had often been speculated in "Here Piggy!", the official Snapoker magazine, that the longest official Snapoker game, which was played in 1979 and lasted for 186 hands, would never be surpassed (incidentally, this 186-hand game was concluded when the fourth placed player lost his marbles and started the biggest Snapoker fight ever seen). Not only did the 2002 ISC final surpass the 186-hand record, it guaranteed that this new record could never be beaten again, only equalled. How many hands were played in the 2002 ISC final?

### Hint

In each hand there are a total of 10 points on offer, so after any given hand the total of all four players' scores must be a multiple of 10.### Answer

There were 207 hands dealt in all.In each hand of Snapoker there are a total of 10 points on offer, so after any given hand the total of all four players' scores must be a multiple of 10.

The highest total of all four players' scores such that the individual scores are still all less than the 518-point winning mark is 2060 (eg. 517, 516, 514, 513 or some other similar combination), which corresponds to 206 hands. This would mean that on the 207th hand one of the players would finally and inevitably win the game.

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