September 6, 1999
Problem of the Week

Class Conscience
adapted from a problem by Christopher McColl     in the September 1999 issue of Games

John Handley High trains its students to be trustworthy, respectable citizens of Winchester;   however, it takes some time for them to get to that point.

In fact, ol' Mr. P, who has been at Handley as long as anyone can remember, has noticed the following tendencies among the student body:

1. Freshmen always lie.
   
   
2. Reflecting their standing as "second-class" citizens, sophomores will always lie unless they are the second ones to speak in a conversation.
   
   
3. John Handley Juniors only lie if they are the third ones to speak or if their sentence begins with a J.
   
   
4. Seniors at Handley never lie.

To test the validity of these observations, Mr. P recently brought four randomly chosen students into his computer lab for a talk. Their names were Fred, Sophie, Julius, and Selena. As it happened, no two of them were in the same graduating class. Mr. P asked each student to tell which class another student belonged to. They answered as follows:


• Fred: Julius is a sophomore.
• Sophie: Selena is a senior.
• Julius: Sophie is a freshman.
• Selena: Fred is a junior.

Mr. P realized that with this information, he could determine what grade each student was in. Can you?

Solution to the Problem:

Julius is the freshman.
Sophie is the sophomore.
Fred is the junior.
Selena is the senior.

To solve this logic problem, try the process of elimination.
Since seniors always tell the truth, assume one of the four Handley students is a senior, and then that student 's statement must also be true. Continue until you find a contradiction or until it works out.

Assume Fred is the senior. Then it follows that Julius is a sophomore. Since sophomores lie unless they speak second, it follows that Sophie is not a freshman; therefore, she must be the junior. Since Sophie is the second one to speak and she is a junior, she must be telling the truth which means Selena is the senior and that contradicts our assumption that Fred is the senior.

Similarly, you can reason that Sophie and Julius can not be seniors because they lead to contradictions.

Assume Selena is the senior. Then Fred must be the junior. Since Fred's sentence starts with a 'J', and since he is the junior, he must be lying, so Julius is NOT a sophomore. Therefore, Julius is the freshman and Sophie must be the Sophomore. If Julius is the freshman, he must be lying, which fits since Sophie is not the freshman. Since Sophie is the sophomore, she is telling the truth because she speaks second, and this fits since it was our assumption -- Selena is a senior.

Correctly solved by:

1. Tom Marino	Winchester, VA
2. Elizabeth Cotter	Oak Hill, VA
3. Angie Cunsolo	Winchester, VA (Shenandoah University)
4. David Powell	Winchester, VA
5. Matt Schroeder	Williamsburg, VA (College of William & Mary)
6. Kaveh Sadegzadeh	Williamsburg, VA (College of William & Mary)
7. Si Schiavone	Winchester, VA
8. Jia Ran	Rome, Italy (St. Stephens High School)
9. Jon Pence	Winchester, VA
10. Ryan Throckmorton	Winchester, VA
11. Debbie Robayo	Winchester, VA
12. Chip Crawford	Winchester, VA
13. Richard Mocarski	Winchester, VA

Send any comments or questions to: David Pleacher