Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

This premise of the student's is sound:

If we haven't had the test by end of Thursday's class, then we'll know in advance it must be on Friday."

The conclusion the student draws from it is not:

"So we can't possibly have the test on Friday, or we'd know in advance."

The premise includes the qualifying phrase "by end of".

This means that if the students haven't had the test before the qualifier kicks in (eg, at the beginning of Thursday's class), they won't know in advance whether the test will be held that day or the next...in which case Friday remains in contention.

Foundation collapses, house collapses.

"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

Offline

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

The only logic, of all I've seen, that I accept is that of bobbym.

So I give him 5 votes. That's not what is usually thought of as democracy, which I abhor. I'm all for meritocracy, though.

I believe that Friday remains in contention, but not because of this logic.

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Bob's Friday exclusion reasons are the same as any given till now only stated differently.

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,762

**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.**

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi bobbym

Did you read my post about the advantage of students who can always expect the test?

*Last edited by anonimnystefy (2012-03-23 21:11:44)*

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi all,

Every time I post I think I've got this sorted and then someone posts back and there are still doubts. So, I'll have one last go and then I'm giving up on this thread.

It is Saturday, now, here in the UK and, on Sunday, I'm busy with something else, so I'll wait until after that.

At some time between Monday at 0101 gmt and Friday at 2359 gmt I will make another post. So it will definitely be on Monday, or Tuesday, or Wednesday, or Thursday, or Friday. But I'm not saying which of these days it will be and you won't know in advance which day it will be. But I will post.

Now I'm going quiet on the subject for a while.

Bob

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

That's the best to go bob.I just think it should be 0001gmt Monday

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,762

Hi anonimnystefy;

**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.**

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Why?

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

Offline

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

bobbym, I took the liberty of reading your hidden text - I suppose that is not a heinous crime.

I agree with your logic couched in wisely guarded and provisional terms, not your conclusion that Friday is out (as I have stated in post #53), and with your perceptions that this is not necessarily a matter of logic at all, having a clear answer. The vagueness of the terms used by, and the situations described by, the student, allow for different points of view.

The subject has revealed Bob's inventiveness, the envelope method and now this simulation of the actual event in real life - way to go!!!

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

Offline

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

Bob Bundy's next-week posts bid fair to make the most exciting event in decades.

I feel free to make the following predictions already:

1. I personally will certainly not know anything in advance.

2. Neither will Bob, regardless of his present or future intention: there is no way he can guarantee the truth of "But I will post.", except as a statement of present intent and not future reality.

And if we start hedging statements with "if"s" or unwarranted assumptions, then we'll be back to square one.

Also I shall not be in the least surprised if the test falls on the Friday, and nobody knows it in advance. Of course they may claim to have known after the event, but that will be a hollow claim.

Just my take!

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,762

**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.**

**Online**

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bob,

Xlnt!! Terrific practical tactic!

The day of your post - Mon, Tue, Wed, Thu or Fri - will be a complete surprise to me...unless you haven't posted by the end of Thursday, in which case I'll know in advance that you'll be posting Friday (although then I'll have to make sure that I check in here right on midnight GMT on Thursday to make sure of beating your Friday's post).

The student of course will conclude that you won't post at all, and therefore won't be keeping an eye on the clock.

Looking forward to next week! Well, you can't look backward to next week, can you? (except for Marty and Doc)

*Last edited by phrontister (2012-03-24 12:53:15)*

"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

Offline

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

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

Hi everyone.

Bob Bundy's next-week posts bid fair to make the most exciting event in decades.

Oh wow! The responsibility. I cannot live up to that! Sorry.

But, by way of compensation, I have managed to track down a copy of the Professors Test which you will find at

http://www.mathisfunforum.com/viewtopic … 98#p206098

Bob

Ps A few loose ends.

anonimnystefy said he would prefer that I start my timing from 0001 GMT. I realised I needed to be precise about the timing. Members log in from all over the world and it could happen that, when I am in one day, someone else is one day ahead or behind me. So I thought Id specify Universal Time as it is a common standard around the world and easy for me as I live so close to Greenwich. But, the UK changes into British Summer Time on 25th March. I have to get a piece of paper to work out whether to add or subtract an hour. So I added an hour just to be on the safe side. I couldnt be bothered with the end time as I knew I wouldnt be posting on a Friday anyway . If we got to late on Thursday with no post youd all have been inundating the MIF server with triumphant posts that you knew when Id be posting!

gurthbruins then said

Neither will Bob, regardless of his present or future intention: there is no way he can guarantee the truth of "But I will post.", except as a statement of present intent and not future reality.

This is, of course, correct. I had intended to add a get-out clause along the lines of providing no act of God prevents me, but I forgot. Having been so definite that I would post next during the week, I couldnt go back and make corrections or someone might accuse me of cheating.

As it happens, that was nearly the case, twice!

Firstly, I opened the boot (trunk) of my car, intending to remove my laptop. But I completely forgot to do this, and so left my laptop in a readily stealable position for about 10 minutes. But the angels were watching over me and no one did.

Then, another disaster! Last night (0400 bst) the place I was staying had a fire and we all had to march outside whilst the fire crew put it out. So once again, the precious laptop was at risk. This morning I made my decision. Too risky to wait for event number three; best to post as quickly as possible. And I have. What can go wrong now? Hope that doesn't mean the MIF server will go on the blink. Sorry MIF.

Bob

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

Offline

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

Interesting! I myself am getting tired of this woolly problem, it seems less appealing now. I think I'll abandon it, though it has been interesting. I am preparing to launch a proper mathematical problem, one with a definite solution and no semantics, shortly.

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

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

I think this is a cleverly-constructed logic puzzle that has a logical solution.

I also agree with Bob's solution, which is the same as mine, though expressed a little differently.

I've enjoyed (and am still enjoying) trying to put together a convincing argument - which hasn't worked, so here's another go at it:

The construction of a building-block tower begins with a foundation block, and blocks are added on top of those that are standing. Any level fails if any lower level fails.

The student's reasoning is such a construction: each conclusion, other than the first, relies on the status of all prior conclusions being 'TRUE'.

My flowchart attempts to demonstrate this concept. You'll notice that the building-block construction of the questions mirrors the building-block construction of the student's conclusions. Accordingly, the answer to all parts of those questions must be "Yes" for any applicable days to be eliminated.

The ridiculous nature of those questions highlights the student's flawed reasoning.

EDIT: My flowchart is wrong, so please ignore it (I can't delete or edit the image).

The student makes an unsound argument for the end of Wednesday's class by relying on a conclusion that only pertains to the end of Thursday's class, and continues that thought into previous days. That's like using faulty blocks for the tower, all 'supported' by a non-existent foundation.

In optical illusions our perception is affected by influencing factors that are not necessarily valid, which is the case with this puzzle. The crafty puzzle setter has diverted our attention from the truth by reasoning in a reverse (abnormal) direction in time, adding credence to it all by beginning with a true and easily-comprehended conclusion.

My conclusion is that only the foundation level is valid, and the rest of the building therefore collapses.

The prof wins.

*Last edited by phrontister (2013-05-04 15:16:42)*

"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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Can any of you see what I was talking about earlier?I could guess that the Big post was gonna be today but then if it's not then I will prepare for.the post to be tomorrow.

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

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi anonimnystefy,

Can any of you see what I was talking about earlier?

Which post or posts do you mean?

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi phro

anonimnystefy wrote:

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.

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi anonimnystefy

I think you left some options out, and that they should be these:-

If the prof doesn't give the test on

- Monday, then they can expect it on Tuesday, Wednesday, Thursday or Friday;

- Tuesday, then they can expect it on Wednesday, Thursday or Friday;

- Wednesday, then they can expect it on Thursday or Friday;

- Thursday, then they'll know for sure the test will be on Friday.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

That logic can be applied as well.It's all in the favor of the students.

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

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

But the student who's doing the talking says, So we can't have the test at all. He says that before any of those days have arrived.

At that point, before test week begins, the students actually have no idea which day next week the test will be held (despite what that one student has theorised).

This is exactly what Bob's test has shown...no one has any concrete idea of the timing of Bob's post day. None of us have said, So Bob won't post at all before the start of this week, nor during any day this week has anyone said they knew in advance which day Bob would post.

Personally, from the start, and despite Bob's assurance to the contrary, I didn't think he'd post this week and would put that down to 'human fallibility' or some such. But my opinion is purely a psychologically-oriented guess, and nothing to do at all with the logic that this logic puzzle requires to solve it.

*Last edited by phrontister (2012-03-30 02:59:40)*

Offline

**alta ego****Member**- Registered: 2012-03-30
- Posts: 9

hi guys,

You seem to be missing something.

In post 57 bob said he would post during the week but you wouldn't know when.

In post 66 he posted. It was a Tuesday. Nobody predicted that.

He also said "So, I'll have one last go and then I'm giving up on this thread."

So he is clearly not going to come back to this thread again.

Case closed.

alta ego

Offline

**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi alta ego,

*Last edited by phrontister (2012-03-30 10:31:29)*

Offline