When can the test be given?

[Steven G]

You are taking a math class that meets Monday through Friday. You teacher announces today (for Denis: assume today is a weekday) that she will be giving an exam next week but no student will have advance notice as to when it will be given. Which day or days, if any, can the exam be given?

 

[Otis]

You are taking a math class that meets Monday through Friday. You teacher announces today (for Denis: assume today is a weekday) that she will be giving an exam next week but no student will have advance notice as to when it will be given. Which day or days, if any, can the exam be given?

What is the meaning of when?

Is it "which week"?

Is it "the time of day"?

Is it "the day of the week"?

Is it something else?

Also, assuming that all of the teacher's students received today's "advance notice" of next weeks exam, does the part of the announcement that stated no student would receive advance notice preclude the exam from being given at all?

 

[Steven G]

What is the meaning of when?

Is it "which week"?

Is it "the time of day"?

Is it "the day of the week"?

Is it something else?

Also, assuming that all of the teacher's students received today's "advance notice" of next weeks exam, does the part of the announcement that stated no student would receive advance notice preclude the exam from being given at all?

By when, I mean which day next week.
By advanced notice I mean that a student (or students) will not be able to walk into class any day next week knowing that the test will be given that day. If somehow a student(s), for example, knows that the test will be on Wednesday prior to Wednesday's class, that will be considered advanced notice.

 

[Ishuda]

You are taking a math class that meets Monday through Friday. You teacher announces today (for Denis: assume today is a weekday) that she will be giving an exam next week but no student will have advance notice as to when it will be given. Which day or days, if any, can the exam be given?

Ob liv i ous ly only on a day they didn't know whether there would be a test. So it couldn't be Friday, since it would not have happened yet on Monday-Thursday and Friday would be the only day left and thus there would be advance notice.

But wait a second. If it can't be on Friday, it must be on Monday through Thursday. EXCEPT, it can't be on Thursday since it would not have happened yet on Monday-Wednesday and Thursday would be the only day left and thus there would be advance notice.

But wait a second. If it can't be on Thursday or Friday, it must be on Monday through Wednesday. EXCEPT, it can't be on Wednesday since it would not have happened yet on Monday or Tuesday and Wednesday would be the only day left and thus there would be advance notice.

But wait a second. If ...

Thus, assuming the teacher always tells the truth (as they see it), something catastrophic (either in general or to the teacher) will happen between now and Monday to keep the test from occurring.

 

[Ishuda]

Depends. If "today" is Friday, then soonest advance
notice can be given is following Monday, so test can
be given from Tuesday to Friday.
You're a kinda weird teacher Jomo

Did we both read the same question? "...but no student will have advance notice ..."

 

[Steven G]

The test can not be given.

My logic prof had no idea what to do when I made this point as he was handing out an exam. As a logistic he could not give the test (and gave everyone 100%)and hated me (and I mean hated me!) for the rest of my time in his class and while I was at the college. After he learned that I was a math major he hated me even more. In the end I won since I earned an A in his class. And boy did I earn that A because I am sure he tried not to give it me.

The story goes further. My math professor who told me about this paradox found out that I used it on my teacher and he too was furious with me. I guess my logic professor told everyone in the math department what I did. I always put my head down when my math professors announced an exam.

And you nice people allow me to tutor here.

Did I tell you how I got into trouble while I worked in the tutoring lab? The precalculus students needed to find a composite function that equals h(x). So naturally I told the students in the lab to simply use f(x)=x and g(x)= h(x). I even told them it did not matter which way they composed them! In the lab I helped them do the problem correctly but for exam purposes I told them to use the trick I mentioned. Faculty knew it must have been me when a handful of students did this on exams. My reasoning why I did this was clear--this composite function of f and g was equal to h, ie it worked for all h(x) and it was easy.



Now as teaching faculty I show them the trick but make it clear that they can't use it on the exam