Logic Problems by Michael Keller

Euchre

Four friends (Bob, David, Harry, and Joe) were playing euchre, a card game played with a 24-card deck containing ace, king, queen, jack, ten, and nine in each of the four suits (spades and clubs (black), hearts and diamonds (red)). The deck is dealt out evenly among the four players. From the clues below, can you determine the full names of the players (last names, in no particular order, are Blackwood, Cavendish, Foster, and Phillips) and the six cards each player received on this particular deal?

(1) One player held the ace and ten of clubs.
(2) Joe held the nine of clubs and also one of the black jacks.
(3) Phillips held the jack of hearts; David held the jack of clubs.
(4) Blackwood held all four kings; Bob held the queen of hearts; Cavendish held both black queens; Harry held the ace of hearts but no other aces. All four players are named in this clue.
(5) One player held the jack of spades and both red tens.
(6) Neither Bob nor Foster held the queen of diamonds.

Grandmaster Tournament

In the latter stages of an international chess tournament, six players still had a chance to win, and in the next-to-last round these six were pitted against each other in three separate games. The six players have four different first (Boris, Dmitri, Igor, and Pavel) and last (Alexandrov, Kuznetsov, Petrov, Sergeev) names, come from four different cities (Moscow, Omsk, St. Petersburg, and Volgograd), and have four different favorite openings (French, Nimzo-Indian, Ruy Lopez, and Sicilian). From the clues below, can you determine the full name, hometown, and favorite opening of the two players involved in each game?

(1) Three players are named Igor; three are named Kuznetsov, three come from Moscow, and three prefer the Ruy Lopez.
(2) Dmitri Sergeev's opponent, who isn't from Omsk, likes the French.
(3) The player from Volgograd faced the player who likes the Sicilian; neither player is Petrov.
(4) No two players among the six share more than one characteristic in common (e.g. at most one player from Moscow is named Igor).
(5) Each pair of players facing each other have none of the four characteristics in common.
(6) Pavel likes the Nimzo-Indian opening best.

Cereal Display

The local grocery store is displaying sixteen kinds of breakfast cereal in a display of four shelves, each shelf containing four different cereals, so that the boxes are arranged in a rough 4x4 square. The cereals come in four flavors (sugar, honey, chocolate, and fruit), four grains (wheat, rice, oats, and corn), and four shapes (stars, squares, flakes, and loops). From the clues below, can you determine which cereal is in each position?

(1) The four most expensive cereals, including Sugar Oat Stars, are on the top shelf.
(2) The cereal directly to the left of the sugar flakes is a rice cereal.
(3) No shelf contains two cereals of the same flavor, grain, or shape. No two cereals with the same characteristics are vertically aligned.
(4) The cereals on each shelf are more expensive than those on the next lower shelf. The cereal at the right end of the lowest shelf is an oat cereal, but not flakes.
(5) No two cereals share more than one characteristic in common; for example, there is only one chocolate oat cereal.
(6) Fruity Wheat Loops are on the second shelf from the top, directly below Sugar Oat Stars.
(7) The cereal at the left end of the top shelf is flakes, but not fruit-flavored.
(8) Oat flakes are less expensive than the chocolate oat cereal, which is less expensive than the fruity squares.

Solutions

Portions of this article previously appeared on the Games Cafe (www.gamescafe.com) in 2000; that site is no longer in operation.