Mathematics

[Azat]

Dear Domino, I am sorry but my question was less a math question than a trick question.

 

The answer that I was looking for was that silly answer of "x-x" being 0 thus my polynomial being 0.

[Sip]

I thought I did but you got me back! Very good recovery I think you have a very good point that I was not thinking about at all. I had just assumed that all variables represented finite values.

 

I think I understood everything you said except that line. Can you please clarify?

 

I agree now that in the general case, if you don't specify finite ( alpha < a < beta, alpha < b < beta, ... , alpha < z < beta, for a finite alpha and beta) then that polynomial is not well defined ... i.e. you could have an inf*0 type of a a situation.

[Guest Fadi]

Sip

 

A little mistake I mean a form of b/0(here b is arbitrary chosen nothing to do with the b of the a, b, c etc...), that the product will end up with a non determinated form like 0/0

 

Azat, yes still if it is a non determinated form the x-x complify the equation even more, since we can end up with a non determinated form and have to lift off this non-determination something that is impossible

 

[ March 09, 2002, 07:58 AM: Message edited by: Domino ]

[Guest Fadi]

Lets brake more head

 

Since you don't know what a, b, c etc... are what proves us that after the multiplications we will not end up of having this form (bla...bla...bla... (x-x))/(bla...bla...bla.. (x-x)) thats a form 0/0 in the equation, but we can lift off this non detrmination since (x-x)/(x-x) equal 1, we will end up with another type of multiplication that has taken away this x-x...

 

So you see, this x-x dosent say anything it just complify more the equation, since now we have to find every form of non determination and we should only be left with the determinated forms, and there is no any powerfull super computer even not the one that has beaten Gasparov that will be able to give us the possibilities

 

Now have I convinced you ?

[Guest Fadi]

Harout, I have one for you.

 

There is one "figure" that is a rectangle and a triangle in the same time.

 

That would mean that the internal angles of 180 will equall 360

 

I want that you give me this figure its angle (for the triangle) and its mesure relation with the rectangle.

 

Thats durty mathematic

[Azat]

Okay Sip,

Last week I only had two strands of hair on my hear and I lost one on the previous problem and the last one fell off on this one with the encoding. Plus Domino is hunting for me to break my head.

 

I know we are looking for a one-way function which for a given X will return a Y, but knowing the Y would be super hard to figure out the X, but I cannot think of the function

 

Need help. I think I have been out of school for too long now.

 

Where is Harut when you need him.

[Sip]

Oh they don't teach you stuff like this in school! Ok I'll slowly give the answer

 

Solution to Coin Toss among untrusted parties

... it has to do with prime factorization. It is very hard to find out the prime factors of a number ... especially if it is very big. It basically comes down to checking things one by one! So if the number is huge, you have many many things to check which will basically take "forever".

 

But, it is relatively easy to find (generate) really big prime numbers. I am not too familiar with the math involved, but I know they can do it since basically crypto relies on it. So if you are the person tossing the coin, you generate 3 huge prime numbers. If the answer is head, you multiply 2 of them and send it. If the answer is tails, you multiply all 3 of them and send it!

 

The key is, that when I have the number that you sent, it would be very hard for me to figure out what it's factors are (i.e. to check to see if it has 3 prime factors or 2 prime factors). However, later on, when you provide me with the factors, I can simply check to see if I only need to multiply 2 of them to get the answer or three of them (heads or tails)!

 

Pretty amazing huh?! Again I am not a crypto expert but I am told that if you can find a way (an algorithm) to do prime factorization very quickly, you will basically break most major encryption schemes. It's probably a little more complicated than that though

 

So since you have no more hair left, I can just throw out as many problems as I want right?

 

So here's another one. The previous was trusted communication ... this one is shared secrets:

 

Shared Secrets Problem

Suppose you and I don't trust each other. But, we have to keep a piece of information, like a password to some account. There is a third party that we both trust. So now, the problem of the third party is to give out that piece of information (let's say it's a number) to both of us, such that neither one will know what the real information (like the password) was, on our own. But both of us together will be able to recover it. This means, come up with a scheme to split a piece of information (a big number) between 2 people, such that neither one on their own can figure it out ... but both together can recover it when they need to.

 

Note: There are many ways to do the above. So as long as you can show your method will work its great! Also, have in mind that the general form of this question is having n people sharing a secret, such that k of them can get together and recover the secret. I have heard this general case but don't have a good solution. If anyone has any ideas, let me know!!! (there could be an answer somewhere but I haven't looked). However, I do have a scheme in mind for the simple case above which I think works... oh and my answer doesn't deal with prime numbers (I re-read this whole thing and realized that it may seem like the problems are related ... they may be but I am not sure!)

 

[ March 09, 2002, 07:49 PM: Message edited by: Sip ]

[Azat]

very cool. I like that one.

[Azat]

Dear Sip, I was telling this puzzle to one of my cousins and he immediately knew about it. They had studies in a Stat class and it is called the "Peruvian coin flip".

[Sip]

Wow! Now we know a name for it

[Harut]

here is a question for you guys to think over.

 

you have an angle of 19 degrees.

how can you divide it into 19 1 degree angles using ONLY a straight and a compos.

[Sip]

Ok Harut jan, I really give up. I just have a feeling this is one of those things that don't have an answer! (have been thinking about it on and off for a few days now)

 

Can you measure distances with the straight edge? Can you mark things on it? If so, then I have more work to do but with a simple straight edge and a compass, I don't think I can split 19 degrees into 19 1 degree angles

[MosJan]

HArout jan - uremn mi hat compos es vertsnum mi shish el Conyak Tel@ indznits galsi es mer mot menq qez k@batsatrenq te inchpes

 

de yete compos ogtagortsel gites qez mi harts - inchpes karor es ogtagortsel compos imanalu hamar voski e metar@ te voch.

 

De hima asa

 

[ March 29, 2002, 05:37 PM: Message edited by: MosJan ]

[Sip]

Mos jan, du metar@ dur indz, yete yes het dam kez, du kimanas vor voski chi

 

Composen el togh Harut@ pahi ir mod

[MosJan]

OK harts chi var@ handipi

[Harut]

Ok, Sip, i'll just give the answer.

 

here it is.

 

you take the compass and draw a circle, whose center is the vertex of the angle.

then you put one end of the comass on one intersation of circle and angle, and the other end on the other intersation.

(i hope you're following me so far)

then you draw 19-degree-arcs aroud the circle.

 

HERE IS THE TRICK.

19*19=361

 

so each time you complete on circle, you get 1 degree ahead.

 

you are done when you go around 19 times.

 

that's it.

 

i hope i explained it right.

[Harut]

Mos jan, du hastat mi ban kharnum es. es im asats compass@ nshanakum a "karkin". du yerevi "koghmnatsuytsi" het es, ha?

yete ha, uremn espes.

 

koghmnatsuyts@ jisht teghn es berum, heto metagh@ dnum es hyusis tsuyts tvogh slaqi dimats. yete slaq@ khakhtvets uremn, metagh@ KAROGH a voski lini.

[Guest Fadi]

LOL... this thread is still continuing...

 

I have read your thing Harut, but still you cut it with 1,003 degrees not 1

 

[ March 30, 2002, 03:18 PM: Message edited by: Domino ]

[Guest Fadi]

SHish... I just understood it, Shish... Harut, your explanation was even harder then my English LOL

 

Ah and if you ask what the hell is this 1,003, its the precision of my compass

 

[ March 30, 2002, 03:37 PM: Message edited by: Domino ]

[Sip]

Wow Harut ... I love that problem! It is very very cool. You can't imagine how long I spent on it

[Guest Fadi]

Now Harut. I tried it, and came to the same point I started it.

 

Lets me explain you why.

 

I told that my compass had a precision of 1,003, to be more exact 1,0028, each time I open it and lose it on this case 0,0028.

 

That mean that when I have the angle of 19 degrees, taking it with my compass it makes 19.0028, and since there is 19 of them, it makes 361.0532, then I have to do it 360 times in order divide all the cercle to 360 pieces.

 

Then, every time I make all the cercle I have 1.0532 degree, when I have done it 360 times, I end up with around 379 degrees separation.

 

A difference of, 19 degree, the same 19 degree that I started with at the biggening.

 

Of course here I suppose you took an R=1 cm, the reference from where my compass was graduated.

[Harut]

on, i took R = 1 km.

 

so, your compass should work almost perfect.

[Guest Fadi]

LOL Harut you go me one that...

 

But my compass just broke out, and my other compass has this 0,0028 add-in error, and this independent of an R as reference... Now what can I do ?

[Harut]

i'll tell you what to do

stop getting in my nervs and start thinking about this problem.

===============

 

Suppose a clock is perfectly accurate, but has only an hour hand, no minute or second hand. What is the exact time when the hour hand is pointing at the 22 minute mark?

[Harut]

here is one of my favorite problems, though i still don't get it, even when i read the answer.

 

see what can you guys do.

======================

 

SOME MONKEY BUSINESS: Hanging over a pulley is a rope. At one end of the rope is a sand bag and at the other end is a monkey. The weight of the monkey is the same as the weight of the sand bag. The rope weighs 4 ounces per foot.

 

The sum of the ages of the monkey and the monkey's mother is 4 years. The monkey's weight in pounds is the same as the mother's age in years.

 

The mother is twice as old as the monkey was when the mother was half as old as the monkey will be when the monkey is three times as old as the mother was when she was three times as old as the monkey was.

 

The weight of the rope and the sand bag is one and a half times the weight of the monkey. How long is the rope?