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[QUOTE="primrose, post: 7157096, member: 1036998"]
Someone in my casino posed this to me and I found it a nice thing to think about. You need to know the rules of Omaha (specifically that you [B]must use[/B] [B]exactly 2[/B] of your 4 cards for the 5-card hand) but you don't need to be good at the game to solve this. Note that it's not easy, so you might need some time.

[B]Puzzle: [/B]You're holding :9h4: :3c4: :3s4: :3h4: . What boards give you the nuts (i.e., the guaranteed strongest possible hands -- no split pots)?

There are three solutions. Well, three [I]groups[/I] of solutions, some of them allow you to switch some cards around to get essentially the same solution but a slightly different board. But the three groups are very different from each other.

Solution 1 (the easiest): [SPOILER]QUADS: Board is :9d4: :9s4: :9c4:  + any two cards that don't allow for stronger quads or a straight flush. An example is  :as4: :kh4:  but there are probably thousands of other combinations. These are all the first group.[/SPOILER]

Solution 2 (harder): [SPOILER]FLUSH: Board is exactly :ah4: :kh4: :qh4: :jh4: :10h4:, giving you the unique 9-high flush. This one doesn't have any variation, only this exact board guarantees you the nuts.[/SPOILER]

Solution 3 (hardest): [SPOILER]FULL HOUSE: Board is :2d4: :2h4: :2s4: :2c4: :3d4: , giving you the 2-2-3-3-3 full house. This solution is unique as well.[/SPOILER]
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