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

bobbym wrote:

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.

Oops, Wednesday is starting to look decidedly dicey...

... the slower we go, the further we'll get, as the tortoise said to the hare.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

I think I know what's wrong . Everything is in the favor of the students. If he doesn't give it on Monday then they can expect it on Tuesday . If he doesn't give it on Tuesday then they can expect it on Wednesday. If he doesn't give it on Wednesday then they can expect it on Thursday. If he doesn't give it on Thursday then they can expect it on Friday .

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Not exactly. Since the last day is out so is the one before it. The professor is not stupid he is never going to pick Friday. He also is never going to pick Thursday. He also is never going to pick Wednesday. The difference in how the day of the test is picked. Randomly or through strategical thought. One is a logic problem the other a game theory problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Still they can expect it whenever he gives it.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Expecting does not count. What gurthbruins is saying is that it is not possible for the professor to choose a day. There is an argument that the students will always be sure of the day of the test.

I am not yet going that far but if the professor wants to bet his money against me and he rationally chooses Friday, Thursday or Wednesday then I am going to win because I will always be able to predict his test day before it happens.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

Wednesday dead and buried already - I didn't think we were going to get so far so soon ...

But seriously, I think bobbym is onto something here. Random picking is logically out, because it amounts to Russian roulette, the prof will have to rely on his luck to vindicate himself. God help him if the random picker chooses Friday or Thursday, because he's going to look very, very stupid... so I am inclined to think also that this is not a logic problem really, more a philosophical, semantic problem to do with the meaning of words like "know".

Imagine trying to set up a machine that could perform all the parts of the professor's role. And make his claims about "who" would "know" what. I don't see how such a machine could be constructed.

So my answer to the riddle is that nothing can be known, ever. The world might end tomorrow, so the professor has no right to say the test will happen at all. And equally the students will never "know" anything anyway. But I'm not really satisfied with that either.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Hi;

I agree randomly picking the day can not guarantee an end to the last day problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi

I have received inspiration from an unexpected source. I was watching "Fool Penn and Teller". A magician called John Archer managed to fool the pair with a 5 envelope trick. And that gave me the idea for explaining this puzzle.

At the weekend the professor buys 5 envelopes. He writes MONDAY on the first, TUESDAY on the next and so on.

He also prepares 5 slips of paper. On 4 of them he writes NO TEST TODAY and on the 5th he writes TEST TODAY.

He puts a NO TEST TODAY slip into the FRIDAY envelope. He shuffles the remaining slips and puts one in each of the other envelopes without looking.

So the day for the test is now fixed. One envelope contains the TEST TODAY slip and it's labelled on the outside with the day.

The students are told to turn up on Monday with a pen and their lucky exam mascot ready to do the test. The professor picks a student who comes out and opens the MONDAY envelope in front of everyone and shows the slip. If it says TEST TODAY the professor gives out the test papers and they get on with it. If it says NO TEST TODAY they get on with something else and come back on Tuesday, to repeat the performance. The professor picks another student to open the TUESDAY envelope and they carry on like that until they do the test.

By Thursday they will have done the test. They have no way of knowing which day it will be; even the professor doesn't know as he didn't look when he put the slips in. So no giveaway clues. He knows it won't be Friday, but the students don't. So the day of the test is a complete surprise.

Professor - 1 student - nil

Bob

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

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

Interesting, but by my reckoning I make the score about 5 - 5, and I myself am voting for both sides. (so far)

*Last edited by gurthbruins (2012-03-22 19:57:21)*

*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: 3,847

Excellent, Bob!

You've replaced the puzzle's plausible-sounding reasoning with a very simple, easy-to-understand and pertinent illustration that evades the crafty author's nose hook that was designed to lead us down the garden path.

Using your forward-direction strategy it is easy to deduce that only Friday can be eliminated from test day options (but only if the test hasn't been held by the end of Thursday's class).

"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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi gurthbruins

by my reckoning I make the score about 5 - 5,

but you seem to be assuming that democracy applies in mathematics.

Given the number of times i've seen it that would mean, for example,

Thanks phrontister,

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi bob

are there numbers a,b,c and d the such that:

?*Last edited by anonimnystefy (2012-03-23 07:25:25)*

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi bobbym

*Last edited by anonimnystefy (2012-03-23 09:47:57)*

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

There is still an infinite number of them, can you see why?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

nope.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

here's an additional restriction:

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Now do you want to hear my comments?

I sure wished you had posted this question in another thread. This is an active thread with gurthbruins' question.

But in answer to your latest question I believe there is an infinite number of solutions here to.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi bobbym and Stefy,

Oh dear. I hadn't intended to spark off another question. I was just trying to make the point that mathematical truth is independent of the number of people who agree with it. I've had lots of pupils who needed to revise their understanding of how you add fractions because they thought you can add the tops and add the bottoms for all fractions. It hadn't occurred to me that it might occasionally be true.

But Ok; it's an interesting divertion, so why not move Stefy's question to a new thread and clear this one back to the original question.

I'm working on the definitive answer (apparently my two previous one still have doubters). Watch this space.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Hi Bob;

I am afraid that I can not move part of a thread only a whole thread can moved. You did nothing wrong, I made the mistake of answering instead of asking him to post in a new thread.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

You're both wrong.I was the one who was supposed to post that question in another thread.Sorry about this.

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

So do it. That way each can re-post and then delete the wrong post version. That's equivalent to moving part of a thread only.

I could copy and paste for you but I don't think I can make a post and attribute it to someone else. And wouldn't want to even if I could!!

And now I'm going to log off so I can think about the professor's test.

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Ok,see you later :-)

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

OK, back to the professor.

My envelope method shows that a real world situation can be constructed with the rules as stated and the professor right. Therefore, the student must be wrong.

There must be a flaw in the argument. In fact, there are lots of them.

(it is Thursday evening) AND (we haven't had the test yet) => ( the test is on Friday)

This contradicts the axiom (you won't know in advance when it is)

so (it is Thursday evening) AND (we haven't had the test yet) must be FALSE.

So if we assume it is Thursday evening then it follows that (the test cannot be on Friday)

(it is Thursday evening => the test cannot be Friday) is TRUE.

The whole is TRUE but you cannot dissect the statement and say that bits of it are therefore also TRUE such as

(it is Thursday evening) and such as (the test cannot be Friday)

The student then argues

(It is Wednesday evening) AND (we haven't had the test yet) => (the test cannot be on Thursday OR Friday)

But this only follows if we accept that (it is Thursday evening) is TRUE and it cannot be both Thurday AND Wednesday.

So we logic statements of the form

A => B and C => D therefore C => B AND D where A and C are mutually exclusive.

And so it continues, assumptions are made about which day of the week it is, together with different assumptions about which day it is, which are put together to reach FALSE conclusions.

And if you are still in doubt about this, look again at post #3. The test is held on Wednesday and the students ARE surprised. Surely, then it is clear that the professor is right and the student is sadly wrong.

Bob

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