You start with a standard deck of cards. Each card is assigned a numeric value from 1 to 52 as follows:

A through K of Clubs = 1 through 13
A through K of Diamonds = 14 through 26
A through K of Spades = 27 through 39
A through K of Hearts = 40 through 52

Each player draws two cards and calculates the cube of the sum of the values of the two cards. Each player then selects five or less non-zero digits from their answer to form their Poker hand. Hands are evaluated solely on the digits, 1 is low and 9 is high, and there are no suits involved. For example: One player draws the 4 of Clubs (4) and the 6 of Diamonds (19); 4 + 19 = 23, 23^3 = 12167, the player has a pair of 1's. A second player draws the Ace of Dimaonds (14) and the Ace of Clubs (1); 14 + 1 = 15, 15^3 = 3375 and she wins the hand with a pair of 3's.

Given these rules, what is the best possible Poker hand a player can have and how many possible combinations of cards will yield that hand?

The best possible poker hand that can be generated in "A Strange Game of Poker" is a full house, i.e., 88877.
This hand is generated from 92³ = 778688.
There are only six pairs of cards that will sum to 92. They, both Hearts, are:

• A (40), K (52)
• 2 (41), Q (51)
• 3 (42), J (50)
• 4 (43),10 (49)
• 5 (44), 9 (48)
• 6 (45), 8 (47)

Posted by Dej Mar on 2009-08-11 18:08:41