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## Question

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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## 11 answers to this question

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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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I though this topic has been posted some time ago...

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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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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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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

Dr P got told 7200

Dr S got told 171

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Have worked out the solution

Ill give away a clue

Dr P got told 7200

Dr S got told 171

96 and 75....but why?

Edited by Nothanks
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96 and 75....but why?

I made a 89x89 table, and calulcated the product of all the numbers.

I removed all numbers which has a product which appeared in the able only once ( because if he was told one of those products he would know the numbers from the start, this removes about half 4095 posibilities

From the remaining numbers sum them all, and remove all the numbers which have a unique sum (becuase Dr S would know the 2 numbers on his first go)

Do these 2 more times..

Do the products one more time and only 1 number combination will be unique, and because he says he knowns what it is, this numbers produce must be his.

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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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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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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.

You have the same info as Dr N so guess you could say you are him.

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I used a spreadsheet and a macro I wrote.. I will send the spreadsheat to you (openoffice) format, however I dont think the macro will work.. I will also try and conver to excel.

There are a few sheet

Sheet 1: a list of all the numbers combinations and products

Sheet 2: a list of all the numbers combinations and sums

Sheet 3: a list of all the numbers combinations: a 1 means active, 0 invalid combernation

Sheet 4: Sheet 1 * Sheet 3 (removes inavtive numbers from the list)

Sheet 5: Sheet 2 * Sheet 3 (removes inavtive numbers from the list)

Sheet 6: Searches Sheet 4 for doubles of products, if a double is found puts a 1, else puts 0

Sheet 7: Searches Sheet 5 for doubles of sums, if a double is found puts a 1, else puts 0

Sheet 8: Looks for differences between sheet 3 and 6

to use:

Goto sheet 3 and fill all with 1's

#i had a macro to do this part

Goto sheet 6 and copy the grid(not headers) onto sheet 3 (to remove numbers which cant be the answer)

Goto sheet 7 and copy the grid(not headers) onto sheet 3

Goto sheet 6 and copy the grid(not headers) onto sheet 3

Goto sheet 7 and copy the grid(not headers) onto sheet 3

goto Sheet 8 and look for the number 1 (the numbers which are cancelled out this iteration)

the excel file was well over 2M.. sorry cant upload it

EDIT: i zipped it

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