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Only One Hand (Posted on 2005-04-11) Difficulty: 2 of 5
In a game of Texas Hold'em, all 5 community cards are dealt, and the three remaining players simultaneously say, "Well, there's only one hand that can beat me."

How can this situation arise? Assume that the players do not lie.

Here, "one hand" means a unique combination of 2 cards, out of the (52 choose 2) = 1326 possible ones.

For those unfamiliar with the basic rules of Texas Hold'em: each player has two face down cards, and there are five face up cards on the table. Each player makes the best possible 5-card poker hand using any of the 5 community cards and his 2 private cards.

See The Solution Submitted by David Shin    
Rating: 4.2857 (7 votes)

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Hints/Tips Comments | Comment 9 of 31 |
People should pay special attention to the definition of hand given in my problem statement. 

Here's a restatement of my puzzle: 

All three remaining players simultaneously say, "IF your hand beats mine, then I can tell you exactly what two cards you are holding."

Also, to address Charlie's earlier post, the poker hand can be created using any 5-card subset of the 7 cards (5 public cards + 2 private cards).  This means that 0, 1, or 2 private cards can be incorporated.

Nobody has yet submitted a valid solution.

  Posted by David Shin on 2005-04-11 18:31:22
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