[Guest]

There was a teacher that liked to give his class an opportunity for extra credit quizzes if they could solve a riddle he gave them in class. One fateful Friday he told his class this:

“Next week there will be a pop quiz. I can promise you that you will not know the day of the quiz until the beginning of class on the same day of the quiz. If you can reasonably prove me wrong, you will not have to take the quiz and I will give you an A on it.”

There was one student who approached the teacher after class that Friday, talked with the teacher for a few minutes about the quiz, and the next week he never had to take the quiz but still got an A on it as the teacher had promised.

Assuming that the class meets in the middle of the day for 1 hour, Monday through Friday, what did the student say to the teacher to avoid taking the quiz and still get an A on it?

Note that the student was able to convince the teacher based on the teacher’s own stipulations given above.

[Guest]

The teacher made this announcement on a Friday so the student reasoned that the pop quiz would be given next Friday. The reasoning behind this is that it was Friday when the teacher made the announcement and the teacher said the pop quiz would be given next week, 7 days from Friday - thus next Friday. Also, the teacher said "you will not know the day of the quiz until the beginning of class on the same day of the quiz." This was said on Friday, the same day the quiz would be given the next week.

[preflop]

I'll take a shot

That the quiz would have to be on Monday (or more accurately no day meets the teacher's stipulations) because ...

1. I could not be on Friday, since if they haven't taken the quiz by Thursday, then on Thursday they would know the quiz would be given on Friday, thus before the beginning of class on the day of the quiz.

2. Likewise it could not be on Thursday, since we have already established Friday is not a valid option, the same rules apply to Wednesday/Thursday as applied to Thursday/Friday. Meaning that if they have not taken the test by Wednesday then Thursday must be the day because we know Friday can't be.

3. Continuing on, Wednesday cannot be the day because the same logic would then be applied to Tuesday

4. How about Tuesday then, well the test can't be Friday, Thursday, or Wednesday - so if we did not take it on Monday, then the same logic applies - so it can't be tuesday.

5. Well that leaves Monday i suppose but not really since this student knows it must be Monday so give the student the A now and be done with it.

[Guest]

There would be no day next week that would work.

Friday - would be know as soon as Thursday came without a quiz

Thursday - would be know since Friday is invalid, as soon as Wednesday came without a quiz

Wed - ..

Tues - ..

Monday - Since you know it can't be any of the other days it has to be monday, therefore making it known which day the quiz was on, so

No day will work.

[Guest]

Well, we can definitely rule out Friday - otherwise everyone would know it would be on Friday. There's not much more than that. We could "almost" say it wouldn't be on Thursday because if it got to be Thursday, they would know it wouldn't be on Friday and would therefore know it would be thursday. But this logic gets too thin the further back we go.

[Guest]

I think you guys got the gist of this one (blades, preflop, and tbrophy). Good Job. What could the teacher say as a rebuttal to the student, if anything?

[Guest]

He can probably say,

"If you indeed know when the quiz will be given, 5 minutes before class begins, tell me that we will be having the quiz that day. If you are right, I'll give you the A."

If everyone tells him before class on Monday, he'll just announce the quiz in class on Tuesday. If nobody tells him on Monday, he'll just announce it in class on Monday. There's no way for them to really know.

This is assuming they only have one guess. They can't say "I know the test is Monday", then when he doesn't give it on Monday, they turn around and say "I know the test is Tuesday."

[bonanova]

This is a classic riddle, perhaps most famously cast by Martin Gardner as the "Unexpected Hanging".

A prisoner was told he would be hanged nest week, on a day that could not be anticipated.

His lawyer made the above arguments to show the execution could not therefore take place at all.

He was hanged the following Wednesday!

Any day would have worked, actually.

Once the lawyer made his case, every day qualified as a day that could not be anticipated.

The executioner simply chose Wednesday.