- 25 Apr '04 10:50Hi folks. This is a quite hard one, took me long time to figure it out. Hope not everybody knows it yet. Have fun.

1. The Penguin says to t he Icebear: I know a sum X which is calculated of a and b so a+b=X , but I don't know what a and b are.

2. The Icebear says: I know a product Y which is calculated by the factors a and b so a*b=Y . I don't know which numbers a and b are, but I knew that you wouldn't know either.

3. The Penguin replies: Well if you say that, than I know the solution which numbers a and b are.

4. The Icebear says: OK, so if you say that, than I also know what a and b are.

Which numbers are a and b?

Yes it's the same a and b in a+b=X and a*b=Y and no, it can not be any number, and yes, Penguins and Icebears may meet somewhere between Arctic and Antartic to talk about stupid riddles. Sorry if the english isn't the best, but should be no matter to the riddle... - 25 Apr '04 11:16

In English we call them 'polar bears'.*Originally posted by Kandinsky***Hi folks. This is a quite hard one, took me long time to figure it out. Hope not everybody knows it yet. Have fun.**

1. The Penguin says to t he Icebear: I know a sum X which is calculated of a and b so a+b=X , but I don't know what a and b are.

2. The Icebear says: I know a product Y which is calculated by the factors a and b so a*b=Y . I don't kn ...[text shortened]... tupid riddles. Sorry if the english isn't the best, but should be no matter to the riddle...

I think the answer is a=b=2 (assuming they have to be counting numbers). Statement 2 indicates that Y is composite (otherwise the polar bear would know the numbers). This is sufficient for the penguin to work out a and b, so it must be that there is exactly one set of numbers which sum to X and have a composite product. The only number for which this is true is X=4, and hence a=b=2. - 25 Apr '04 14:40OK thank you, it's 'Polar Bear' than.

Reading you're answer made me think some minutes because remembering the brain cracking work I had with this riddle I couldn't imagine it to be solved so easily (and differing from my solution), and after reading my previous post over and over again I now have to seriously apologize for 2 major mistakes in the riddle as I wrote it down.

First of all I (shame on me) completely missed to say the integers are to be >1 (and <100 if that is for any help) so 1<a,b<100. I'm sorry.

The second and even worse thing is that I mixed up the order in which the Polar Bear and the Penguin appear.

The final and correct version of the riddle I sadly messed up before is:

1. The Polar Bear is telling the Penguine: I know a product X which is calculated by the factors a and b so a*b=X , but I don't know what a and b are.

2. The Penguin says: I know a sum Y which is calculated by a and b so a+b=Y . I don't know which numbers a and b are, but I knew that you wouldn't know either.

3. The Polar Bear replies: Well if you say that, than I know the solution which numbers a and b are.

4. The Penguin says: OK, so if you say that, than I also know what a and b are.

I apologize for any inconvenience. :'( - 25 Apr '04 17:02

Ok, this time assuming that the animals know that a and b are at least 2:*Originally posted by Kandinsky***OK thank you, it's 'Polar Bear' than.**

Reading you're answer made me think some minutes because remembering the brain cracking work I had with this riddle I couldn't imagine it to be solved so easily (and differing from my solution), and after reading my previous post over and over again I now have to seriously apologize for 2 major mistakes in t ...[text shortened]... if you say that, than I also know what a and b are.

I apologize for any inconvenience. :'(

Statement 2 indicates that Y is not the sum of two primes, otherwise the Penguin would not know that the Polar Bear did not know what the numbers were. ()

This is sufficient for the polar bear, so X must be such that exactly one of its factorisations into two numbers >1 does not have a sum which is the sum of two primes. In addition this must give an a and b whose sum is not shared by any other a and b that satisfy the previous conditions, as otherwise the Penguin wouldn't be able to work out the answer. ()

I think that the answer is 4 and 13. However, it's quite likely I made a mistake on the way, and even if it's correct, I don't know if the answer is unique.

Good puzzle, Kandinsky! - 25 Apr '04 17:44
*Originally posted by Acolyte*

I think that the answer is 4 and 13. However, it's quite likely I made a mistake on the way, and even if it's correct, I don't know if the answer is unique.!

Very good, that's correct!

Neither am I completely sure, but as far as i checked it that should be unique at least for all integers <100.