Let's discuss Mathematics

[ParadigmShifter]

Because P said he didn't know what the numbers are.

 

[Mise]

I believe I have narrowed it down to this list of possible combinations...

65,80
75,80
80,85
75,88
75,92
80,95

This list would satisfy P but not S... How does S know what the number is, when he finds out that P knows his number?

HMMMMMMMM.....

 

[Mise]

Because P said he didn't know what the numbers are.

I know, but what rule do you use to discount it?

 

[ParadigmShifter]

Statement #1

EDIT: So it's an oversimplification to say that mn must be a product of 2 primes for P to not know the numbers involved.

 

[Mise]

Yeah I get that statement 1 discounts it, what I meant was, what does that tell you about m and n? What rule can you apply to m and n that would discount such a number? You're right that it's an oversimplification to only discount the primes due to (i); what's a better rule?

 

[Truronian]

I've got as far as checking statement 3 with (4,13)... statement four looks to be a whole load of analysis without some kind of program. Might attempt it once I've made some more Ikea furniture.

 

[Mise]

I'd love to know from ThinkTank (or anyone who has looked up the answer) if one of the above combinations is the answer. Please?!?!?!?

 

[Truronian]

I'm gonna look it up, can't be bothered with it any more...

EDIT: Nope Mise, 'fraid not.

 

[Mise]

God damn mongrel surprisingly large testicles. Imma start over....

 

[ParadigmShifter]

Truronian has the right answer

Here's a link to a site that brute forces it Brute force and maths shouldn't go together

Spoiler :

http://everything2.com/title/Mr+Product%27s+and+Mrs+Sum%27s+Quiz

 

[Mise]

I GOT THE ANSWER I GOT THE ANSWER!!!

It's 4 and 13. It's the only possibility left after working through the things. The trick is to realise that, for the question to make sense, P and S must have been told only certain numbers. I will go through the steps in more detail in a mo...

STEPS:

Spoiler :

1) Draw up a giant list of all numbers defined in the question (i.e. 2 <= m <= n <= 99)
2) from that list, multiply m and n
3) Create a table of all m,n where the product is unique (i.e. all m,n that violate (i) ). Call it table B.
4) Create a table of all m,n where the product is not unique (i.e. all m,n that satisfy (i) ). Call it table C.
5) From table C, create a new table (D) that contains all m,n where m+n in table C is not also in table B. (This satisfies (ii).)
6) From table D, do the same thing we did in step 3, i.e. eliminate all non-unique products of m,n. This satisfies (iii), because P could not possibly have known the answer, unless it was in this list.
7) Lastly, find the only remaining combination of m,n whose sum is unique -- this is your answer. This satisfies (iv), because S could not possibly have known the answer if he received any other sums in that list.

If anyone wants to see the spreadsheet, I am uploading it to Google Docs now. Link imminent...

Link: https://docs.google.com/leaf?id=0Bz...2QtYWFiZGRlZjc0NTJh&hl=en_GB&authkey=CK38jZQD

 

[Truronian]

I GOT THE ANSWER I GOT THE ANSWER!!!

It's 4 and 13. It's the only possibility left after working through the things. The trick is to realise that, for the question to make sense, P and S must have been told only certain numbers. I will go through the steps in more detail in a mo...

If anyone wants to see the spreadsheet, I am uploading it to Google Docs now. Link imminent...

That's what I did, though by step four it was getting way to big a job for my scrap of newspaper...

Plus I got lucky in chosing the right numbers; I suspected 4 and tried numbers to go with it.

 

[ParadigmShifter]

Is a brute force approach a good mathematical exercise?

Is the 4 colour theorem (reduce it to loads of cases and brute force them) a good proof?

I say NO! Discuss...

 

[dutchfire]

Well, what's the difference between a brute force approach on 100*100 possibilities and brute forcing:
x<0 (which is trivial)
x=0 (which follows by definition)
x>0 (which is left as an exercise to the reader)

Splitting a problem up into all possible cases and proving them one by one is certainly an acceptable proof.

 

[ParadigmShifter]

Yeah it's an acceptable proof, but not an elegant proof.

Mathematics should have aesthetic appeal in my opinion.

 

[Mise]

My spreadsheet was pretty pwn though.

 

[dutchfire]

Yeah it's an acceptable proof, but not an elegant proof.

Mathematics should have aesthetic appeal in my opinion.

Why then do most mathematicians look so aesthetically dis-appealing?

 

[ParadigmShifter]

I dunno, the maths society recruitment girl was properly smokin' She even brought a cake to the Hawkwind gig we went to on mushrooms.

 

[Truronian]

There was a rather attractive lassie in one of my seminar groups a couple years ago. She offered me paper once.

Good times.

 

[ParadigmShifter]

Maths society recruitment girl who liked Hawkwind probably best looking girl I've ever seen. She was a bit chubby though. She was lovely.