September 26 Problem Solving

College Applications, p. 99 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.

College Applications, p. 99 No student’s first name begins with the same first letter as her or his last name. No student’s first name ends with the same letter as the last letter of her or his 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 there.

Solving Step-by-Step 1. The first thing you must do is determine the other three names and colleges. The clues give you a lot of information: the first names Hank, Alan, and Gladys are mentioned in clues 2, 3, and 4; and community college, university, and private college are mentioned in clues 2, 3, and 5.

2. Create the matrix.

3. Read the clues and mark the matrix. Hank starts with “h” and ends with a “k,” so his last name couldn’t be Burbank. Alan’s last name couldn’t be Gunderson because it ends in an “n.” Gladys’s last name couldn’t be Gunderson because it starts with a “g,” and it couldn’t be Collins or Williams because they end in “s.”

3. Read the clues and mark the matrix. Cathy’s last name couldn’t be Collins because it starts with a “c.” Mark 1-5 on the matrix. We can now determine that Gladys’s last name is Burbank. Indicate that on the matrix.

2. Create the matrix. X1 X X1 X1 O X1 X1 X

3. Read the clues and mark the matrix. Using Clue 2 Hank and Williams did not go to the community college. Since Hanks and Williams were referred to as two people, Hank’s last name couldn’t be Williams. Indicate 1-2 with X2 on the matrix.

2. Create the matrix. X2 X1 X2 X X1 X1 O X1 X1 X X2

3. Read the clues and mark the matrix. Using Clue 3 Alan and Collins did not go to the university because the clue refers to three people who live on the same street. Alan was not Collins. Show 1-2 with X3

2. Create the matrix. X2 X1 X2 X X3 X1 X3 X1 O X1 X1 X X2 X3

Currently 2. Create the matrix. X2 X1 O X X2 O X X3 X1 X3 X1 O X1 X1 X X X O X2 Known results: Gladys Burbank Hank Collins Alan Williams Cathy Gunderson X3 Alan has to be Williams because that was the only space left. This means we can X the Cathy-Williams space. Cathy must be a Gunderson, which forced Hank to be Collins. We now know all first and last names. Write that in your known results area.

2. Create the matrix. Re-read clues 2 and 3 and use the known results. Based on what we know 2. Create the matrix. X2 X1 O X X2 X2-3 O X X3 X1 X2-3 X3 X1 O X1 X1 X X X O X2 X2-3 Known results: Gladys Burbank Hank Collins Alan Williams Cathy Gunderson X2-3 X3 Re-read clues 2 and 3 and use the known results. Neither Hank Collins nor Alan Williams went to the community college. Clue 3 now reads “Alan Williams, Hank Collins, and the student who went to the university all live on the same street. The other student lives two blocks away.” So, Williams and Hank did not go to the university.

3. Read the clues and mark the matrix. Using Clue 4 Gladys and Hank live next door to each other. Using clue 3, who lives on the same street as Hank and must go to the university? Gladys Show on the matrix with O4 and mark the X4s also.

2. Create the matrix. X2 X1 O X X2 O5 X2-3 X5 O X X3 X1 X2-3 X5 X3 O5 X1 O X1 X1 x4 x4 O4 x4 X X O O X x4 X X X2 x4 X2-3 X Known results: Gladys Burbank Hank Collins Alan Williams Cathy Gunderson X5 x4 O5 X X2-3 O4 X3 x4 x4 O5 X5 X Using Clue 5 The last clue says that Hank did not go to the private college. So Alan must have gone to the private college, and therefore Hank went to the state college. Answers: Gladys Burbank — university Hank Collins — state college Alan Williams — private college Cathy Gunderson — community college