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:
- Freshmen always lie.
- Reflecting their standing as
"second-class" citizens, sophomores will
always lie unless they are the
second ones to speak in a conversation.
- John Handley Juniors only lie if
they are the third ones to speak or
if their sentence begins with a J.
- 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?
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:
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 |