Logic Puzzles

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

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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