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Problem of the Week

Problem D

Order Four Cards

Four playing cards are placed in a row, from left to right. Each card is of a different suit. One card is a club (\(\clubsuit\)), one card is a diamond (\(\diamondsuit\)), one card is a heart (\(\heartsuit\)), and one card is a spade (\(\spadesuit\)), not necessarily in that order. There is a different integer between 1 and 10, inclusive, on each card (an ace is read as a 1).
Using the following clues, determine the exact order of the cards, from left to right, including the suit and number.

  1. The heart and the spade are immediately beside each other, in that order, from left to right.

  2. The diamond is not the first (leftmost) card, and the club is not the fourth (rightmost) card.

  3. The 7 is somewhere to the left of the club and the 3 is somewhere to the right of the club.

  4. The two cards whose values are still unknown add to nine.

  5. From left to right, the cards are arranged from largest to smallest.

Club card Diamond card Heart card Spade card