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This question suggested itself to me – and I found a solution – after I solved Can you balance this poker deck?.

Take out two aces from the standard 52-card deck. Your challenge is to partition the remaining 50 cards into ten poker hands, one each of all the popularly recognised types:

  • Royal flush
  • Straight flush that is not a royal flush
  • Four of a kind
  • Full house
  • Flush
  • Straight
  • Three of a kind
  • Two pair
  • One pair
  • High card

In addition, your solution must satisfy two more constraints.

  • The seven non-flush hands must each use all four suits.
  • The sum of card values in each hand must be at least 34, counting 2s to 10s as face value, jacks as 11, queens as 12, kings as 13 and aces as 14.

Good luck.

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  • $\begingroup$ Does the first condition apply to each and every one of those seven remaining hands, or just all of them combined must use all four suits? $\endgroup$ Mar 10 at 22:42

3 Answers 3

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I think this would work

Royal flush: 10S, JS, QS, KS, AS
Straight flush: 7C, 8C, 9C, 10C, JC
Four of a Kind: 5C, 5D, 5H, 5S, AC
Full House: 3C 3H 3S KD KH
Flush: 2D 6D 7D 9D JD
Straight: 6C 7S 8H 9H 10D
Three of a Kind: 4C 4D 4S 10H QH
Two pair: QC QD 2H 2S 6H
One pair: 8D 8S 2C 7H 9S
High Card: 3D 4H 6S JH KC

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My own solution:

Royal flush: AS KS QS JS 10S
Straight flush: 10C 9C 8C 7C 6C
Four of a kind: 5S 5H 5D 5C AC
Full house: 3S 3D 3C KH KD
Flush: QH JH 6H 3H 2H
Straight: JC 10H 9S 8D 7D
Three of a kind: 4S 4H 4C QD 10D
Two pair: 7S 7H 6S 6D QC
One pair: 2S 2D KC 9D 8H
High card: JD 9H 8S 4D 2C

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A bit late to the party, but I enjoyed working this out.
Based on card images linked by @EricDuminil on SE's Board & Card Games.
I removed the Aces of Hearts and Clubs.

Here is my first solution

enter image description here

I found 1760 solutions before my C program crashed :)

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