Guest Posted August 8, 2008 Report Share Posted August 8, 2008 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 I though this topic has been posted some time ago... Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 9, 2008 Report Share Posted August 9, 2008 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 (edited) 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 August 9, 2008 by Nothanks Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 96 and 75....but why? Congrads on your answer, it is what I got! 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 9, 2008 Report Share Posted August 9, 2008 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2008 Report Share Posted August 10, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 10, 2008 Report Share Posted August 10, 2008 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 Quote Link to comment Share on other sites More sharing options...
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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?
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