Story of Four High School Friends

Four high school friends, one named Cathy, were about to go to college. Their last names were Williams, Burbank, Collins, and Gunderson. Each enrolled in a different college, one of them being a state college. 

From the clues below determine each person's full name, and the college he or she attended.

1. No student's first name begins with the first letter as her or his last name, and no students first name's last letter is the same as his last name's last letter.

2. Neither Hank or Williams went to the community college.

3. Alan, Collins, and the student who went to the university all lived on the same street. The other student lived two blocks away.

4. Gladys and Hank lived next door to each other.

5. The private college accepted Hank's application, but he decided he could not afford to go there.

Here is ANALYSIS of the story! 

Analysing The Story of Four High School Friends

What was the story?

GIVEN DATA : 

First Name : Hank, Gladys, Cathy, Alan 
Last Name : Collins, Burbank, Gunderson, Williams 
College       :  State College, University, Community College, Private College 

HINTS : 

1. No student's first name begins with the first letter as her or his last name, and no students first name's last letter is the same as his last name's last letter.

2. Neither Hank or Williams went to the community college.

3. Alan, Collins, and the student who went to the university all lived on the same street. The other student lived two blocks away.

4. Gladys and Hank lived next door to each other.

5. The private college accepted Hank's application, but he decided he could not afford to go there.   

STEPS :  

1] Let's make a table like below and fill it as per hints.

  
2] As per Hint (3), we have, Alan, Collins and student going to the university as 3 different students.

3] As per (1), Collins can't be Cathy & as per (4), Cathy can't be at no.3 as in that case no blocks will be left for (4) to be true. Hence Cathy must be at no.4.

4] As per (2), Hank and Williams are two different students. And as per (4), Gladys and Hank must be at 2 & 3 (and anyhow these are only blocks left for them) but order yet to be known. So, Williams is certainly not at 3 or 2. And as per (1), Gladys can't be Gunderson or Collins or Williams & Hank can't be Burbank.  Therefore, Hank must be Collins at 2 and Gladys must be Burbank at 3.

5] Now, as per (1), Alan can't be Gunderson hence must be Williams and Cathy must be Gunderson. 

6] As per (2), neither Hank nor Williams went to community college, hence Cathy Gunderson must be. And as per (5), Hank didn't choose private college hence must have chosen state college while Alan Williams must be in private college.

7] Therefore, the final table looks like as below.