December 1, 2008 in The Puzzlor
Five-by-Five Poker
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https://doi.org/10.1287/orms.2008.06.06
Five-by-five poker is a solitaire poker variant in which a player arranges 25 cards in a five-by-five grid. Each column and each row in the grid represents a poker hand, making 10 hands in total. The object of the puzzle is to rearrange the cards to maximize the summed points from each hand. Hands are awarded points based on the accompanying table:
For example, in Figure 1, the first row contains one pair of Kings (worth one point), the second row contains three Jacks (worth three points), the fourth row contains a straight (worth four points) and the fourth column contains a flush (worth five points). The remaining rows and columns contain no hands of value and are worth zero points. This yields a total score of 13.
Only the following 25 cards may be used: Hearts Q J 9 4, Diamonds A K Q J 9 8 7 6 5 4 2, Spades K J 10 9 4 2, Clubs K Q 9 4.
Question:
What arrangement of cards maximizes the total point value from all 10 hands?
Send your score and card arrangement to [email protected] by Feb. 15, 2009. The submission with the highest score will receive an “O.R.: The Science of Better” Tshirt. In the event of a tie, the winner will be chosen randomly from among the highest scores. Congratulations to Gino Sedano for correctly solving August’s PuzzlOR. Past questions and answers can be found at puzzlor.com.
John Toczek is the AVP Predictive Modeling at Chubb in the Decision Analytics and Predictive Modeling department. He earned his BSc. in Chemical Engineering at Drexel University (1996) and his MSc. in Operations Research from Virginia Commonwealth University (2005).