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### #1

Posted 18 March 2008 - 03:13 PM

A to B: "I don't know what your number is."

B to A: "I don't know what your number is.

A to B: "I don't know what your number is."

B to A: "I know what your number is."

What was the original palindromic number?

### #2

Posted 18 March 2008 - 03:35 PM

Are there three distinct digits in the original number?There are two intelligent people (A and B) and a 5 digit palindromic number (a number that reads the same forwards and backwards). A is told the sum of the digits of the number. B is told the product of the digits of the number. Both A and B know all these details, but not the 5 digit palindrome or the other person's number. They go on to have the following conversation:

A to B: "I don't know what your number is."

B to A: "I don't know what your number is.

A to B: "I don't know what your number is."

B to A: "I know what your number is."

What was the original palindromic number?

Or do we not need to know that?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 18 March 2008 - 03:42 PM

There are two intelligent people (A and B) and a 5 digit palindromic number (a number that reads the same forwards and backwards). A is told the sum of the digits of the number. B is told the product of the digits of the number. Both A and B know all these details, but not the 5 digit palindrome or the other person's number. They go on to have the following conversation:

A to B: "I don't know what your number is."

B to A: "I don't know what your number is.

A to B: "I don't know what your number is."

B to A: "I know what your number is."

What was the original palindromic number?

I don't think there is a unique number ...

### #4

Posted 18 March 2008 - 03:50 PM

Are there three distinct digits in the original number?

Or do we not need to know that?

You don't need to know that.

### #5

Posted 18 March 2008 - 03:53 PM

I don't think there is a unique number ...

### #6

Posted 19 March 2008 - 06:37 AM

### #7

Posted 19 March 2008 - 07:07 AM

### #8

Posted 19 March 2008 - 08:11 AM

I think I have it. Please correct me if im wrong (which I probably am). Well I think that the number is 00000. Am I right?

Sorry, no. If that was the number then the sum would be 0 and the product would be 0. But that's the only combination that can give a sum of 0, so A would know straight away what B's number was...

### #9

Posted 19 March 2008 - 11:02 AM

Sorry for guessing but struggling to see it!

### #10

Posted 19 March 2008 - 02:56 PM

Spoiler for just a guess- did not cover all the bases!!

Sorry for guessing but struggling to see it!

Bad luck. This is the first puzzle I've posted on here and it seems to have people stumped. I don't want to completely give the game away, but to help things along here's a pretty big clue:

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