See if you can figure out the proper ordering. The rules are as follows:
You have a deck of 28 cards: 8 through ace in four suits. Arrange 25 of these cards in the five-by-five grid so that the 12 named poker hands appear in the rows, columns and diagonals. The location of some cards and suits are given.
To make it easiest to solve, I copied the image (right click on the image and "Copy Image") to a powerpoint slide (open powerpoint and Paste). Then I inserted a few text boxes with 8-A of each suit, moving the various permutations. However, you should not need approach the solution with a trial & error methodology.
Click to view my hint if you're interested
On the diagonal from the bottom right is a Royal Flush. We know that it cannot be diamonds (Ad, Qd are already exposed). We know that it cannot be hearts (too many hearts are exposed, yielding more than the 8h,9h maximum to be used). We know it cannot be spades for the same reason (3 spades are already exposed, and at maximum, 2 spades can only be exposed 8s,9s in order to form a Ts-As royal). Therefore, the Royal Flush diagonal must all be clubs.
For the two Four of a kinds, we know that all 4 ranks are needed to form proper quads. Both Four of a kinds intersect the Royal Flush requirement. Moreover, the A, Q, & J are already used elsewhere. Subtracting those possibilities from the quads requirement, we are left with Quad K's and Quad T's.
Furthermore, we know that the Straight requirement involves an 8. Therefore, that straight must run 8-Q, limiting the intersecting quads row to < Q. A good question to ask at this point may be "how can I be sure that the intersecting card between the vertical Four of a kind and the horizontal straight is not the kicker? Well, we know most of the suits of the horizontal Four of a kind, and can see that there are 2 hearts listed already in the first and 4th columns. Therefore, the kicker to the vertical Quads is one of the card that makes up the horizontal Quads.
That should be enough to get you started on the right path...
For the two Four of a kinds, we know that all 4 ranks are needed to form proper quads. Both Four of a kinds intersect the Royal Flush requirement. Moreover, the A, Q, & J are already used elsewhere. Subtracting those possibilities from the quads requirement, we are left with Quad K's and Quad T's.
Furthermore, we know that the Straight requirement involves an 8. Therefore, that straight must run 8-Q, limiting the intersecting quads row to < Q. A good question to ask at this point may be "how can I be sure that the intersecting card between the vertical Four of a kind and the horizontal straight is not the kicker? Well, we know most of the suits of the horizontal Four of a kind, and can see that there are 2 hearts listed already in the first and 4th columns. Therefore, the kicker to the vertical Quads is one of the card that makes up the horizontal Quads.
That should be enough to get you started on the right path...
i need a deck of cards to help think, but dont give the answer too soon
ReplyDelete"For the two Four of a kinds, we know that all 4 ranks are needed to form proper quads. Both Four of a kinds intersect the Royal Flush requirement. Moreover, the A, Q, & J are already used elsewhere. Subtracting those possibilities from the quads requirement, we are left with Quad K's and Quad T's."
ReplyDeleteThis thinking is wrong as the 4 cards can be anywhere in the 5 cards... So even though they cross the Royal flush the card in the quad is not necessarily part of it. The middle horizontal WOULD need to be part of the Royal though otherwise it would have two hearts in it. The vertical quad could theoretically be 9s though. *
*During initial thoughts.
@The Dyer - The horizontal Quads has 2 hearts already associated to it. Therefore, the direct center of the 5x5 grid MUST BE a club, making the cell to its left a diamond. Moreover, the bottom right cell must be a club as well, since it is associated with the royal flush. Given that the horizontal quads "kicker" is a heart, the right most horizontal quad is the kicker to the vertical quads. Based on that assertion, the top right cell on the horizontal quads MUST BE a spade, and is one of the cards that make up the quads. Neither the vertical nor the horizontal quads, as making up a royal flush, can be anything except a T-A. Since A,Q,J are used, K, T are the remaining possibilities. Is that a better statement of my logic? I hope so - sorry if I was unclear the first go around...
DeleteThanks for the puzzle. My coworker and I enjoyed it. It is the Sudoku of poker! 4 of a kind and the full house were the key
ReplyDeleteYup. Once you solve it, you know that you solved it. I wonder if I really need to post the solution...
DeleteYou have to wait for TBC to solve it, of course.
Delete