Brain Teasers
Brain Teasers Trivia Mentalrobics Games Community
Personal Links
Submit a Teaser
Your Favorites
Your Watchlist
Browse Teasers
All

Cryptography
Group
Language
Letter-Equations
Logic
Logic-Grid
Math
Mystery
Optical-Illusions
Other
Probability
Rebus
Riddle
Science
Series
Situation
Trick
Trivia

Random
Daily Teasers
Search Teasers

Advanced Search
Add to Google Add to del.icio.us

More ways to get Braingle...

Mathematicians

Math brain teasers require computations to solve.

 

Puzzle ID:#10150
Fun:** (2.1)
Difficulty:**** (3.16)
Category:Math
Submitted By:rajeshwar*
Corrected By:EnderofGames

 

 

 



There are 4 mathematicians - Brahma, Sachin, Prashant and Nakul - having lunch in a hotel. Suddenly, Brahma thinks of 2 integer numbers greater than 1 and says, "The sum of the numbers is..." and he whispers the sum to Sachin. Then he says, "The product of the numbers is..." and he whispers the product to Prashant. After that, the following conversation takes place :

Sachin : Prashant, I don't think that we know the numbers.
Prashant : Aha! Now I know the numbers.
Sachin : Oh, now I also know the numbers.
Nakul : Now I also know the numbers.

How did they know the numbers?

Open Calculator



What Next?

  
  

See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.

 



Comments

electronjohn*us*
Feb 11, 2003

Very interesting, although extremely hard to solve. That has got to be one of the longest answers posted so far. My hats off to you for all the work you did on this one.
Codammanus
Feb 12, 2003

I'm not a fan of teasers involving primes. However, the level of thought involved in constructing this one is astonishing.
Gizzer*
Feb 18, 2003

He didn't work hard on this one at all. Check out the Mathematicians post under Teasers without answers. Mad-Ade pointed him to another site with this teaser!
smileysteve**
Apr 02, 2003

Huh?
gerdmain
Nov 05, 2003

Is this really the only solution? What about a sum of 65? It can be presented as (2,63)...(32,33). All possible products except (4,61) = 244 have multiple answers.

Also a sum of 89 and the product 1168(16,73) is another solution, and there are many more.
karanw
Nov 20, 2003

Oh...u cant solve this...!
knbrain**
Dec 24, 2004

I got bored reading the answer
Sane**
Mar 23, 2005

Posted by Gizzer Feb 18, 2003

He didn't work hard on this one at all. Check out the Mathematicians post under Teasers without answers. Mad-Ade pointed him to another site with this teaser!



Owned
yevgen
Sep 02, 2006

In fact, sum 29 = 13+16 is also a solution (the smallest solution above 13+4 = 17). The way to make solution unique is to say that the product is less than 200.

Also, the solutoion is very tediously presented. A good way to solve this is the following:

1) the fact that Sachin knew Prashant cannot know the sumbers means that the sum is ODD and also sum munis 2 is composite. Indeed, every even number = sum of two primes (famous Euler's conjecture, easily verified for small numbers).

2) the fact that Prashant knew the answer after that means that his product is uniquely decomposable into two numbers whose sum is ODD. It is easy to verify that this means his product = prime times a power of two (except for 2 itself, since then Prashant would know right away).

3) The fact that Sachin knows as well means that his sum S is uniqulely decomposable as prime+power of two (except for 2 itslef), and also S-2 is not prime.

Now, we go through all numbers of the form (composite+2), and check if they are uniquely decomposable as prime+power of 2.

This way we see 15 (composite) + 2 = 17 = 13 (prime) + 4 (power of 2), but 17-8 = 9 is composite, and 17-16 is 1 which is disallowed. Going thorough other numbers, the next sum like that is 27 (compsite)+2 = 29 = 13 (prime) + 16 (power of 2), but 29-4=25 (composite) and 29-8 = 21 (composite). However, 13*16=2-8, which is greater than 200, so it can be rules out. Going a bit further we see that next number is indeed 63 (composite) + 2 = 65 = 61 (prime) + 4, since 65-8 = 57 (composite), 65-16=49 (composite), 65-32 = 33 (compsite). Once again, though, 61*4 = 244 > 200, so it's out too.
rachayl*
Sep 13, 2006

I'm adding this to my favorites. This is exactly the kind of teaser I was hoping to find when I joined this site. I like thinking about numbers, though I don't have any background in number theory, and solving a prob like this gets me thinking about numbers in all sorts of new ways. Like, I didn't know about Euler's conjecture, but I just spent 20 pleasant minutes conjecturing it on my own!
Hope to find more teasers like this!! Thanks!
teasermaster**
Dec 19, 2006

I thought this one was unsolvable. Way too hard and there should've been a hint!
teasermaster**
Dec 19, 2006

I thought this one was unsolvable. Way too hard and there should've been a hint!
(user deleted)
Feb 02, 2007

To earlier comment - hint probably wouldn't have helped much...

Yah this is crazy hard, but interesting none the less
lolliepupAus
Feb 16, 2007

way...way...too hard.
pating**
Jun 25, 2007

What just happened there? I got lost!!!
javlad27Aus*
Jul 28, 2007

That's the longest answer I've ever seen!
sftball_rocks13*
Aug 27, 2007

wow
um...the answer was longer than the teaser
but...wow
i *never* would have gotten that



Back to Top
   



Online Now: 14 users and 498 guests

Copyright © 1999-2014 | Updates | FAQ | RSS | Widgets | Links | Green | Subscribe | Contact | Privacy | Conditions | Advertise

Custom Search





Sign In A Create a free account