### Brain Teasers

# Rare Snapoker Hands 2

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.

In a game of Snapoker I was playing the other day, my good friend Kasy managed to grab 13 cards that formed an alternating-colours straight (ie. the odd cards were all red, the evens were all black). How many different ways can a 13-card alternating-colour straight be formed from a Snapoker deck? Note that jokers can not be used in forming a straight.

In a game of Snapoker I was playing the other day, my good friend Kasy managed to grab 13 cards that formed an alternating-colours straight (ie. the odd cards were all red, the evens were all black). How many different ways can a 13-card alternating-colour straight be formed from a Snapoker deck? Note that jokers can not be used in forming a straight.

### Answer

There are 32,768 possible ways a 13-card alternating-colour straight can be formed in a Snapoker deck.To form a 13-card alternating-colour straight in Snapoker the following cards can be used:

2 x red aces

4 x black twos

2 x red threes

2 x black fours

2 x red fives

2 x black sixes

2 x red sevens

2 x black eights

4 x red nines

2 x black tens

2 x red jacks

2 x black queens

2 x red kings

Therefore, there are 2x4x2x2x2x2x2x2x4x2x2x2x2 = 32,768 possible 13-card alternating-colour straights that can be formed.

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