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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

*Here's an old classic: I don't know if it's been aired lately.*

The professor said to his class: I'll be giving you a test one day next week, but you won't know in advance which day.

But that's impossible! objected one student. If we haven't had the test by end of Thursday's class, then we'll know in advance it must be on Friday. So we can't possibly have the test on Friday, or we'd know in advance.

That leaves only Monday, Tuesday, Wednesday and Thursday as possible days.

But if we haven't had the test by end of Wednesday's class, we'll know in advance it must be on Thursday, since we have already ruled Friday out. So we can't have the test on Thursday either, or we'd know in advance.

That leaves only Monday, Tuesday and Wednesday as possible days.

But if we haven't had the test by end of Tuesday's class, we'll know in advance it must be on Wednesday, since we have already ruled Friday and Thursday out. So we can't have the test on Wednesday either, or we'd know in advance.

That leaves only Monday and Tuesday as possible days.

But if we haven't had the test by end of Monday's class, we'll know in advance it must be on Tuesday, since we have already ruled Friday and Thursday and Wednesday out. So we can't have the test on Tuesday either, or we'd know in advance.

That leaves only Monday as a possible day. So we'll know in advance that the test will be on Monday. So we can't have the test on Monday either, or we'd know in advance.

So we can't have the test at all.

Who is right, the professor or the student? I have never seen a satisfactory resolution of this paradoxical argument.

*It's the activity of the intelligence above all that gives charm to existence.*

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**amberzak****Member**- Registered: 2012-03-16
- Posts: 80

Well, speaking as a trainee teacher, the professor is always right

Don't think outside the box. Think there is no box

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,603

So he gives it on Wednesday and they are all surprised.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

hi

Of course, I agree with amberzak!

But for reasons of logic too.

The deduction "We've reached the end of Thursday, so it must be on Friday" is sound.

but this does not allow you to deduce anything about earlier days.

Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday". It is always dangerous to keep applying the same logic as the student has done. And MathsIsFun's answer shows why!

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,280

Hi gurthbruins,

I was busily typing up my answer and then saw Bob's reply.

I came to the same conclusion as Bob.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**wintersolstice****Real Member**- Registered: 2009-06-06
- Posts: 122

the way I resolve this paradox is to say that:

the students use the logic to eliminate every possible day, so whichever day it happens it's a a suprise (they didn't see it coming) because they eliminated every possible day:D

Why did the chicken cross the Mobius Band?

To get to the other ...um...!!!

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

I think you're right bob!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**wintersolstice****Real Member**- Registered: 2009-06-06
- Posts: 122

bob bundy wrote:

hi

Of course, I agree with amberzak!

But for reasons of logic too.

The deduction "We've reached the end of Thursday, so it must be on Friday" is sound.

but this does not allow you to deduce anything about earlier days.

Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday". It is always dangerous to keep applying the same logic as the student has done. And MathsIsFun's answer shows why!

Bob

I don't actually agree with this logic because if they reached the end of Wednesday then it must be Thursday because if it was on Friday it wouldn't be a suprise (because if it hasn't happen by the end of Thursday is has to be Friday)

but that's just my opinion:D I have seen another way (apart from my own) of resolving th paradox so I suppose it show there's more than one way to do it:D

Why did the chicken cross the Mobius Band?

To get to the other ...um...!!!

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

wintersolstice wrote:

bob bundy wrote:hi

Of course, I agree with amberzak!

But for reasons of logic too.

The deduction "We've reached the end of Thursday, so it must be on Friday" is sound.

but this does not allow you to deduce anything about earlier days.

Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday". It is always dangerous to keep applying the same logic as the student has done. And MathsIsFun's answer shows why!

Bob

I don't actually agree with this logic because if they reached the end of Wednesday then it must be Thursday because if it was on Friday it wouldn't be a suprise (because if it hasn't happen by the end of Thursday is has to be Friday)

but that's just my opinion:D I have seen another way (apart from my own) of resolving th paradox so I suppose it show there's more than one way to do it:D

I don't agree with this logic either, and I think your objection (your "because") is valid. I have yet to see one way of resolving this paradox.

I would appreciate it if all those who have an opinion about this problem, would state clearly: Do they think the test could be on Friday, yes or no? That I think would be the best point to start tackling this problem thoroughly.

*It's the activity of the intelligence above all that gives charm to existence.*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,280

Hi gurthbruins,

I think the test can't be on Friday.

Edit: I didn't say that right...see next paragraph for explanation.

If the students haven't had their test by the end of Thursday's class they'd know in advance that the test is on Friday (the last day of that week)...hence Friday's elimination in that case.

Friday differs from the other test day options as it is the only day not followed by any other school day that week, with the effect that the elimination rule that works for Friday/Thursday can't automatically be applied to the relationship between other days.

So prior to Thursday's end the option of the test being given on Thursday is still open, and if the professor chose to give the test on Thursday the students would all be surprised.

*Last edited by phrontister (2013-05-04 12:34:23)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

Hi Phrontister,

Notice, in Bob's post, the following:"

Because, for example, at the end of Wednesday the logic is "We've reached the end of Wednesday, so it could be on Thursday or Friday".

"

But you say you think it can't be on Friday, whereas Bob is suggesting that it can be. This difference needs to be settled. If we are to reach agreement.

*It's the activity of the intelligence above all that gives charm to existence.*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

I think that it cannot be on Friday,but it can be on any other day,like MIF has clearly shown in his reply.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

Not if the teacher will not pick Friday. Then Thursday is out too.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

It seems that the later the test, the more impossible it becomes. So MIF seems to be playing it fairly safe by plumping for Wednesday. But is it safe enough? But first let's get the full picture on Friday... because I have a feeling that if Friday goes down the drain, there'll be no stopping the collapse...

*It's the activity of the intelligence above all that gives charm to existence.*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Hi bobbym

Why is it out?

*Last edited by anonimnystefy (2012-03-22 11:22:06)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

If the teacher chooses randomly Monday-Thursday it may or may not be true. I am not sure.

But if the teacher is trying to maximize his chances by playing a strategy,he will never pick Friday. His students know this. If he picks Thursday then when Wednesday comes his student will know for sure it is tomorrow. So he cannot pick Thursday either if both sides are playing rationally.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

But wednesday is still not out!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

Hi;

I am not talking about Wednesday at the moment. I am just saying Thursday is out too, if the teacher plays rationally and never picks Friday.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Well I'm talking about Wednesday now.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

Think about it like this for a second. The teacher we assume picks the date of the test first. It is fixed. If he picks Thursday or Friday the students will know the night before for certain. Perhaps now because he can not pick Thursday and Friday without giving the students advance knowledge, he might not be able to pick Wednesday because on Tuesday the students will know for certain it is tomorrow!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

But he can pick Thursday !

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

The problem is he can never pick Thursday, provided he would never pick Friday.

When Wednesday comes the students have advance knowledge.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,000

Ok so he cannot give it on Thursday but there is no something strange now.They wouldn't be surprised if he gave it on Thursday but they would be surprised if he gave it on Wednesday!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,283

Maybe not. If the professor chose Wednesday on the Friday before, when Tuesday came around the students could deduce the test is tomorrow,since Thursday and Friday are out.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

anonim, I saw you were in a hurry to get onto Wednesday, and now you are going back to Thursday! You're making me nervous! I was going to post

slowly, slowly catchee monkey... "They stumble that run fast" (Romeo and Juliet, if I remember correctly)

but then I saw bobbym's carefully considered post and I thought that would make things clearer ... but apparently not.

And while I was typing this I saw there was another post in the meantime but if I have to abort every time I'll never get a word in...

*It's the activity of the intelligence above all that gives charm to existence.*

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