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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