Chapter 4 Matrix Logic A matrix, or two-dimensional chart helps organize information in a useful way and facilitates eliminating possibilities, which is an important strategy for solving logic problems.
This table shows what classes are offered at each period in River High School.
Example 1. Ted, Ken, Allyson, and Janie (two married couples) each has a favorite sport. The sports are running, swimming, biking, and golf. Determine from the following clues who likes which sport. • Ted hates golf: he agrees with Mark Twain that golf is a good walk spoiled. • Ken can’t run around the block, and neither can his wife. • Each woman’s favorite sport is featured in a triathlon. • Allyson bought her husband a new bike for his birthday for use in his favorite sport.
Example 2. Outdoor Barbecue Tom, John, Fred, and Bill are friends whose occupations are (in no particular order) nurse, secretary, teacher, and pilot. They attended a church picnic recently, and each one brought his favorite meat (hamburger, chicken, steak, and hot dogs). From the clues below, determine each man’s name, occupation, and favorite meat.
Names Occupations Favorite meats
Clues • Tom is neither the nurse nor the teacher. • Fred and the pilot play golf together. The burger lover and the teacher hate golf. • Tom brought hot dogs. • Bill sat next to the burger fan and across from the steak lover. • The secretary hates golf too.
Example 3College Applications Four high school friends (one is named Cathy) are about to go to college. Their last names are Williams, Burbank, Collins, and Gunderson. Each is enrolled in a different college (one is a state college). From the clues below, determine each person’s full name and the college he or she will attend.
Clues • No student’s first name begins with the same first letter as his or her last name. No student’s first name ends with the same last letter of his or her last name. • Neither Hank nor Williams is going to the community college. • Alan, Collins, and the student who is going to the university all live on the same street. The other student lives two blocks away. • Gladys and Hank live next door to each other. • The private college accepted Hank’s application, but he decided he couldn’t afford to go.