45. Five-Card Logic A hand of five playing cards has been dealt from the ranks Ace (1) through Ten. Each of the five cards has a different value (rank). Using the clues below, determine the exact five cards (rank and suit). All four suits appear at least once among the five cards. No three of the cards form a sequence of three consecutive numbers. The total value of the red cards equals the total value of the black cards. The hearts in the hand add up to 12. The even-valued cards total four more than the odd-valued cards. The club is lower in value than the spade. The lowest card in the hand is a diamond. Which five cards were dealt? Added 29 May 2008 Show Hint Show Solution Hint: Start by letting the five ranks be a, b, c, d, e (all different) and translate each clue into an equation or inequality. Pay particular attention to the parity (even/odd) and color conditions to cut down the possibilities quickly. Solution: The five cards are 2♦, 3♥, 6♣, 8♠, and 9♥.
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