Road Trip: Nevada

No road trip would be complete without a stop in Las Vegas! We find ourselves pitted against Lucky Lucas, the reigning world champion at Five-Card Draw poker. In each of four separate rounds of poker, you’ve deduced some partial information about Lucas’s five-card hand that round. Based on that intelligence, how many different hands are possible for Lucas each round?

Note that card order doesn’t matter; a hand of A♥ 3♦ 4♣ 9♠ K♠ is equivalent to K♠ 9♠ 4♣ 3♦ A♥. The numerical value of an ace is 1, a jack is 11, a queen is 12, and a king is 13.


Information Number of possible five-card hands Two-letter code (A=1, B=2, C=3, …)
A full house, where the hand includes at most one diamond, at most one ace, and at most two 2s.
Five red cards that add up to 32, all with distinct numerical values.
Four black cards of the same suit that make a straight (aces always low), plus any one red card.
Four spades and a heart, with a total sum between 12 and 26 (inclusive) or between 46 and 59.


Lucas’s secret word:

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which was fathered by

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