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# A Surprize quiz next week

## Question

A Logic Class Professor declares on Friday: "We're going to have a surprise quiz next week, but I'm not telling you what day... if you can figure out what day it will be on, I'll cancel the quiz."

The students get together and decide that the quiz can't be on Friday, as if the quiz doesn't happen by Thursday, it'll be obvious the quiz is on Friday. Similarly, the quiz can't be on Thursday, because we know it won't be on Friday, and if the quiz doesn't happen by Wednesday, it'll be obvious it's on Thursday (because it can't be on Friday). Same thing for Wednesday, Tuesday and Monday. So it can't be on ANY day, so there's no quiz next week!"

They tell the professor, who smiles and says, "Well, nice to see you're thinking about it."

On Tuesday, the professor gives the quiz, totally unexpected!

What's the flaw in the students' thinking?

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Assumption: it can be any day of the week.

(1) It can't happen on Friday, because it would no longer be a surprise on Thursday.

(2) It can't happen on Thursday, because it can't happen on Friday, and then would no longer be a surprise on Wednesday.

(3) It can't happen on Wednesday, because it can't happen on Thursday-Friday, and then would no longer be a surprise on Tuesday.

(4) It can't happen on Tuesday, because it can't happen on Wednesday-Friday, and then would no longer be a surprise on Monday.

(5) It can't happen on Monday, because it can't happen on Tuesday-Friday, and then would no longer be a surprise.

(6) So the assumption is it won't happen.

(7) So it would no longer be a surprise to have it on Friday (or any day). So (1) [and (2)-(5)] is no longer true.

(8) It can be any day of the week.

(8i) But It can't happen on Friday, because it would no longer be a surprise on Thursday.

(8ii) And It can't happen on Thursday, because it can't happen on Friday, and then would no longer be a surprise on Wednesday.

Etc.

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Since they've ruled out it being on any day of the week, they think they're safe. However, now that they don't expect the test, the Professor can give it to them on any day except possibly Friday, and they'll be surprised!

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A Logic Class Professor declares on Friday: "We're going to have a surprise quiz next week, but I'm not telling you what day... if you can figure out what day it will be on, I'll cancel the quiz."

The students get together and decide that the quiz can't be on Friday, as if the quiz doesn't happen by Thursday, it'll be obvious the quiz is on Friday. Similarly, the quiz can't be on Thursday, because we know it won't be on Friday, and if the quiz doesn't happen by Wednesday, it'll be obvious it's on Thursday (because it can't be on Friday). Same thing for Wednesday, Tuesday and Monday. So it can't be on ANY day, so there's no quiz next week!"

They tell the professor, who smiles and says, "Well, nice to see you're thinking about it."

On Tuesday, the professor gives the quiz, totally unexpected!

What's the flaw in the students' thinking?

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As a teacher you never chose Monday...to many students absent or have a week-end hangover:)! Tuesday is perfect because it gives the teacher Wednesday and Thursday to grade the quiz and post it on Friday!

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The students' backwards induction works only if the professor knew what day he was planning to assign the quiz. If he selected the quiz randomly (say by using a 5 sided die), backwards induction would fail and the students should have seleced a day at random.

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This is a variant of the Unexpected Hanging paradox described by Martin Gardner and others.

It was posted in this forum here:

And here:

Please read these threads, and post any new thoughts here.

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This is a variant of the Unexpected Hanging paradox described by Martin Gardner and others.

It was posted in this forum here:

And here:

Please read these threads, and post any new thoughts here.

Fully agreed with Bonanova, this problem is a classical paradox...

As suggested, my thoughts on the same....

The situation in this problem is a contradiction.

Logic very well explain us, there can't be a surprise test next week as then it won't be a surprise.

But, in real world, a surprise is a surprise, if logically deducible that won't be surprise any longer.

The way Professor has declared about Surprise quiz was totally contradictory on logical basis, it is like saying ' you will have a surprise quiz, tomorrow (logically not sensible).

Being heard about the such a surprise quiz, the students should have taken it seriously ... should have started preparing their subjects... hehehe...

There is a similar paradox. I will like to put here for all you to give a thought...

Once in a town there was a male barber who, every day, shaves every man who doesn't shave himself, and no one else.

Do you think such a Barber could ever exist ?

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Once in a town there was a male barber who, every day, shaves every man who doesn't shave himself, and no one else.

Do you think such a Barber could ever exist ?

...doesn't shave himself, and so shaves himself.

And so doesn't shave himself.

And so shaves himself.

So no.

But for fun:

He doesn't shave himself, and so he shaves himself.

To "shave oneself" means to actually apply razor to stubble.

He applies razor to stubble.

He immediately meets the condition of "shaving himself" and so stops.

Ah, but there was a bit of stubble removed!

Option 1:

And because he stopped, he no longer shaves himself, and so shaves himself (just a bit of stubble again) and stops. He continues this until he is finally clean shaven. This takes about a week to complete. His originally shaved stubble has grown back. And so he is perpetually shaving himself. He loses his barbershop, his house, his wife, his kids hate him, he can't eat, he wastes away, and he dies a sad, lonely man with oddly shaped facial hair.

Option 2:

Because he has removed a tiny bit of stubble, he is forever "one who shaves(shaved?) himself" and so will not shave him(self). He grows a wicked long beard in which birds and squirrels live. He buys a banjo and lives out his retirement days in the foothills of the Appalachians.

Edited by psykomakia
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The "Surprise" has taken place. "You have a surprise quiz next week!" could mean "Surprise! You have a quiz next week."

The students don't have to be surprised the day of the quiz, they have already been surprised by the quiz's existence. So the assumption that it couldn't be on Friday is faulty.

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Fully agreed with Bonanova, this problem is a classical paradox...

As suggested, my thoughts on the same....

The situation in this problem is a contradiction.

Logic very well explain us, there can't be a surprise test next week as then it won't be a surprise.

But, in real world, a surprise is a surprise, if logically deducible that won't be surprise any longer.

The way Professor has declared about Surprise quiz was totally contradictory on logical basis, it is like saying ' you will have a surprise quiz, tomorrow (logically not sensible).

Being heard about the such a surprise quiz, the students should have taken it seriously ... should have started preparing their subjects... hehehe...

There is a similar paradox. I will like to put here for all you to give a thought...

Once in a town there was a male barber who, every day, shaves every man who doesn't shave himself, and no one else.

Do you think such a Barber could ever exist ?

Again...

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May be the barber was a male child.....!!!

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