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11 replies to this topic

### #1 papa

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Posted 09 August 2008 - 12:03 AM

Three mathematicians—Dr P, Dr S and Dr N—were told that two two digit positive whole numbers had been selected. Dr P was given the product of the two numbers, Dr S was given their sum and Dr N was given neither. The following exchange occurred:

Dr P: I don’t know the two numbers.
Dr S: I don’t know them either.
Dr P: I still don’t know the two numbers.
Dr S: Neither do I.
Dr P: Now I know the two numbers.
Dr S So do I.
Dr N And so do I.

What are the two numbers?
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### #2 Nothanks

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Posted 09 August 2008 - 01:33 AM

I can only deduce that it has to be a prime and a composite number, and that the sum can't be arrived at by adding two prime numbers together...I don't have the time to run through the numbers.
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### #3 woon

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Posted 09 August 2008 - 04:05 AM

I though this topic has been posted some time ago...
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### #4 bonanova

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Posted 09 August 2008 - 04:15 AM

Three mathematicians—Dr P, Dr S and Dr N—were told that two two digit positive whole numbers had been selected. Dr P was given the product of the two numbers, Dr S was given their sum and Dr N was given neither. The following exchange occurred:

Dr P: I don’t know the two numbers.
Dr S: I don’t know them either.
Dr P: I still don’t know the two numbers.
Dr S: Neither do I.
Dr P: Now I know the two numbers.
Dr S So do I.
Dr N And so do I.

What are the two numbers?

Are the numbers necessarily different?
Are you sure they're both two-digit numbers?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #5 taliesin

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Posted 09 August 2008 - 10:42 AM

Are the numbers necessarily different?
Are you sure they're both two-digit numbers?

This one is quite hard.. Im working on it at the moment.

Im taking the viewpoint, that i am Dr N ( who knows nothing about the numbers) I Hope that is right.
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### #6 taliesin

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Posted 09 August 2008 - 04:27 PM

This one is quite hard.. Im working on it at the moment.

Im taking the viewpoint, that i am Dr N ( who knows nothing about the numbers) I Hope that is right.

Have worked out the solution

Ill give away a clue

Spoiler for Clue

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### #7 Nothanks

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Posted 09 August 2008 - 08:04 PM

Have worked out the solution

Ill give away a clue

Spoiler for Clue

Edited by Nothanks, 09 August 2008 - 08:08 PM.

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### #8 taliesin

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Posted 09 August 2008 - 10:46 PM

Spoiler for Solution

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### #9 papa

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Posted 10 August 2008 - 12:52 AM

Are the numbers necessarily different?
Are you sure they're both two-digit numbers?

The puzzle was given to me by a friend; he had worked it but gave no info on the numbers having to be different. He did say that the number range is from 10 to 99 which would only include two digit numbers.
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### #10 taliesin

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Posted 10 August 2008 - 12:58 AM

The puzzle was given to me by a friend; he had worked it but gave no info on the numbers having to be different. He did say that the number range is from 10 to 99 which would only include two digit numbers.

I worked it out with doubles allowed and the answer comes out fine
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