### Brain Teasers

# Snapoker Scoring

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 frantic 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.

The other day, I was having a lively game of Snapoker with three friends when, after three hands, my good friend Kasy commented that my score was the only score that was not a prime number. What was my score?

The other day, I was having a lively game of Snapoker with three friends when, after three hands, my good friend Kasy commented that my score was the only score that was not a prime number. What was my score?

### Hint

In each hand there are a total of 10 points on offer, so after three hands the total of all four players' points must be 30.### Answer

I was on 9 points.After one round of Snapoker a total of 10 points have been awarded to the four players, so after three rounds a total of 30 points have been awarded, meaning players' scores must add up to 30.

The lowest score after three hands is 3 (receiving 1 point every hand) and the greatest score is 12 (receiving 4 points every hand). Note also that if one player has a score of 3, the next lowest possible score is 6 (receiving 2 points on every hand). Similarly, if one player has a score of 12, the next highest possible is 9 (receiving 3 points every hand). If however a player has a score of 4 (1, 1 and 2 points) the next lowest possible score is 5 (2, 2 and 1 points). A similar approach can be applied for lowest scores of 5, 6 and 7 and for highest scores of 11, 10 and 9.

Now while there are many possible combinations of points that add up to 30, there are only three combinations where one player's score is not a prime number. These combinations of points are:

3, 7, 9, 11;

5, 5, 9, 11;

7, 7, 7, 9.

In each of the cases above, 9 is the only non-prime and thus must be my score.

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