Mathematicians - Treat for the weekend / might drive you crazy
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(Actually, This is an old problem but just to stop smartsy CPians from using the word "nanosecond" forever let's blast them with it! ). There are 2 integers a and b (Though programmers like i and j more as integers) And two CPian A and B. (The result will decide who are they) Rules of the game ------------------------------- I. 2 <= a,b <= 100 II. A is told the product of a and b III. B is told the sum of a and b. IV. Neither is told the values The cPians conversation ::: ------------------------------- 1=> B: I cannot determine a, b. 2=> A: I cannot determine a, b 3=> B: I already knew that. 4=> A: In that case, I now know them 5=> B: In that case, I too now know a, b. What are the numbers ??? ------------------------------- Is'nt it simple and beautiful ? I can hear you saying " huh! " cheers. "Not everything that counts can be counted..." -Albert Einstein
Interpreting your qu differently gives 4, 13. I think this used to be called "the impossible problem" Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
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explanations are for sissys Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
Guessing two numbers between 2 and 100, gives a probability of 0.02020202020202020202020202020201 chances of getting it correct so it is not. As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.-Albert Einstein
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Guessing two numbers between 2 and 100, gives a probability of 0.02020202020202020202020202020201 chances of getting it correct so it is not. As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.-Albert Einstein
I believe its abit less than that. Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
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(Actually, This is an old problem but just to stop smartsy CPians from using the word "nanosecond" forever let's blast them with it! ). There are 2 integers a and b (Though programmers like i and j more as integers) And two CPian A and B. (The result will decide who are they) Rules of the game ------------------------------- I. 2 <= a,b <= 100 II. A is told the product of a and b III. B is told the sum of a and b. IV. Neither is told the values The cPians conversation ::: ------------------------------- 1=> B: I cannot determine a, b. 2=> A: I cannot determine a, b 3=> B: I already knew that. 4=> A: In that case, I now know them 5=> B: In that case, I too now know a, b. What are the numbers ??? ------------------------------- Is'nt it simple and beautiful ? I can hear you saying " huh! " cheers. "Not everything that counts can be counted..." -Albert Einstein
OK, your post has been up for several hours now. How about posting your solution? Personally, I think the problem is indeterminate, at least without additional constraints.
Software Zen:
delete this; -
(Actually, This is an old problem but just to stop smartsy CPians from using the word "nanosecond" forever let's blast them with it! ). There are 2 integers a and b (Though programmers like i and j more as integers) And two CPian A and B. (The result will decide who are they) Rules of the game ------------------------------- I. 2 <= a,b <= 100 II. A is told the product of a and b III. B is told the sum of a and b. IV. Neither is told the values The cPians conversation ::: ------------------------------- 1=> B: I cannot determine a, b. 2=> A: I cannot determine a, b 3=> B: I already knew that. 4=> A: In that case, I now know them 5=> B: In that case, I too now know a, b. What are the numbers ??? ------------------------------- Is'nt it simple and beautiful ? I can hear you saying " huh! " cheers. "Not everything that counts can be counted..." -Albert Einstein
2 & 3 or vica versa My reasoning the lowest 2 numbers that are not 2 & 2. 1. B: (a x b) = 6 2. A: (a + b) = 5 3. B: a != b and a < 4 and b < 4 4. A: Can only be 2 & 3 5: B: Can only be 2 & 3 :confused: Probably very incorrect... :p [update] Similar to Rui A. Rebelo's solution [update] xacc.ide-0.1-rc3 released! Download and screenshots -- modified at 12:23 Saturday 12th November, 2005
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I believe its abit less than that. Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
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(Actually, This is an old problem but just to stop smartsy CPians from using the word "nanosecond" forever let's blast them with it! ). There are 2 integers a and b (Though programmers like i and j more as integers) And two CPian A and B. (The result will decide who are they) Rules of the game ------------------------------- I. 2 <= a,b <= 100 II. A is told the product of a and b III. B is told the sum of a and b. IV. Neither is told the values The cPians conversation ::: ------------------------------- 1=> B: I cannot determine a, b. 2=> A: I cannot determine a, b 3=> B: I already knew that. 4=> A: In that case, I now know them 5=> B: In that case, I too now know a, b. What are the numbers ??? ------------------------------- Is'nt it simple and beautiful ? I can hear you saying " huh! " cheers. "Not everything that counts can be counted..." -Albert Einstein
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2 & 3 or vica versa My reasoning the lowest 2 numbers that are not 2 & 2. 1. B: (a x b) = 6 2. A: (a + b) = 5 3. B: a != b and a < 4 and b < 4 4. A: Can only be 2 & 3 5: B: Can only be 2 & 3 :confused: Probably very incorrect... :p [update] Similar to Rui A. Rebelo's solution [update] xacc.ide-0.1-rc3 released! Download and screenshots -- modified at 12:23 Saturday 12th November, 2005
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OK, your post has been up for several hours now. How about posting your solution? Personally, I think the problem is indeterminate, at least without additional constraints.
Software Zen:
delete this;Check the clue below that can filter the range of numbers its better to try the other way (backward :) ) I don't like to keep you waiting but some people are still trying. I will post the solution tonight. May be before that you might hit the light bulb moment :) "Not everything that counts can be counted..." -Albert Einstein
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For those who are still trying for the solution here is a clue to drive you more crazy 3=> B: I already knew that. i will post the solution by tonight "Not everything that counts can be counted..." -Albert Einstein
Is A and B necesary CPians? Or can they be other kinds of people too? If the former, my original hunch was perhaps the user id of 2 specific users under 10000 that can be broken down to the requirements... (long shot :) ) xacc.ide-0.1-rc3 released! Download and screenshots
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Is A and B necesary CPians? Or can they be other kinds of people too? If the former, my original hunch was perhaps the user id of 2 specific users under 10000 that can be broken down to the requirements... (long shot :) ) xacc.ide-0.1-rc3 released! Download and screenshots
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(Actually, This is an old problem but just to stop smartsy CPians from using the word "nanosecond" forever let's blast them with it! ). There are 2 integers a and b (Though programmers like i and j more as integers) And two CPian A and B. (The result will decide who are they) Rules of the game ------------------------------- I. 2 <= a,b <= 100 II. A is told the product of a and b III. B is told the sum of a and b. IV. Neither is told the values The cPians conversation ::: ------------------------------- 1=> B: I cannot determine a, b. 2=> A: I cannot determine a, b 3=> B: I already knew that. 4=> A: In that case, I now know them 5=> B: In that case, I too now know a, b. What are the numbers ??? ------------------------------- Is'nt it simple and beautiful ? I can hear you saying " huh! " cheers. "Not everything that counts can be counted..." -Albert Einstein
Is there more than one answer?
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Is there more than one answer?
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You presume? Please see my email to you, and then clarify your presumption. Thanks, David
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You presume? Please see my email to you, and then clarify your presumption. Thanks, David
thanks for the link actually i got what you are saying its the domain which is not mentioned there. If the Domain is 2 to 100 ( which is in this case ) then there is a unique solution If you expand the domain to 2 to 1000 then the there are two solutions :) the problem you sent the link it does not gives any MAX Range only thing it gives is the MIN Range
The Link says:
PUZZLE STATEMENT: A and B are positive integers greater than 1.B Professor Sum "S" knows only the sum of A and B. Professor Product "P" knows only the product of A and B. The following conversation occurs between "S" and "P" "S" says to "P": You don't know A and B. "P" says to "S": Now I do know A and B. "S" says to "P": Now I know A and B as well. What are the values of A and B?
SO TWO SOLUTIONS THERE but in our problem there is only one :) So i think that removes the ambiguity About wraping it the cache page says the problem was
The Link also have:
Assigned: Wednesday, Sept. 25, 2002 Due: Thursday, Oct. 10, 2002
So i think that makes it clear :) , by the way i liked to see that it was an assignment because to find a solution u need to do some exhaust search with some constraints. Cheers "Not everything that counts can be counted..." -Albert Einstein
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thanks for the link actually i got what you are saying its the domain which is not mentioned there. If the Domain is 2 to 100 ( which is in this case ) then there is a unique solution If you expand the domain to 2 to 1000 then the there are two solutions :) the problem you sent the link it does not gives any MAX Range only thing it gives is the MIN Range
The Link says:
PUZZLE STATEMENT: A and B are positive integers greater than 1.B Professor Sum "S" knows only the sum of A and B. Professor Product "P" knows only the product of A and B. The following conversation occurs between "S" and "P" "S" says to "P": You don't know A and B. "P" says to "S": Now I do know A and B. "S" says to "P": Now I know A and B as well. What are the values of A and B?
SO TWO SOLUTIONS THERE but in our problem there is only one :) So i think that removes the ambiguity About wraping it the cache page says the problem was
The Link also have:
Assigned: Wednesday, Sept. 25, 2002 Due: Thursday, Oct. 10, 2002
So i think that makes it clear :) , by the way i liked to see that it was an assignment because to find a solution u need to do some exhaust search with some constraints. Cheers "Not everything that counts can be counted..." -Albert Einstein
As I pointed out in my email, that page gives two solutions where the numbers are both under 100, therefore, as you worded it, it is an ambiguous problem, unless the page is incorrect? David
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As I pointed out in my email, that page gives two solutions where the numbers are both under 100, therefore, as you worded it, it is an ambiguous problem, unless the page is incorrect? David
Well , i try to clearify The Domain actually restricts the unique solution though i understand both the solutions is in the range and that makes it feel that both are correct. but the solution space is not so its not what it looks like , if the solution space is 2 - 100 you will never get the other solution unanimously. and ALSO it contradicts the problem it self becuse if there are two solutions then how come the the two persons are sure about the anwser they will still have to decide between the two solutions right ? I just wrote this without thninking -- modified at 19:18 Sunday 13th November, 2005
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Well , i try to clearify The Domain actually restricts the unique solution though i understand both the solutions is in the range and that makes it feel that both are correct. but the solution space is not so its not what it looks like , if the solution space is 2 - 100 you will never get the other solution unanimously. and ALSO it contradicts the problem it self becuse if there are two solutions then how come the the two persons are sure about the anwser they will still have to decide between the two solutions right ? I just wrote this without thninking -- modified at 19:18 Sunday 13th November, 2005
You are being unclear.
Quartz... wrote:
but the solution space is not so its not what it looks like , if the solution space is 2 - 100 you will never get the other solution unanimously.
I think you meant "if the solution space is 2 - 100 you will never get the other solution by itself." Yet both the solutions occur 'by themselves' in the solutions given in that page, and I cannot see ANY difference in the solution spaces between your posting of the problem and the posting on that page.
and ALSO it contradicts the problem it self becuse if there are two solutions then how come the the two persons are sure about the anwser they will still have to decide between the two solutions right ?
Wrong. Each of them has a clue to the answer, and when A knows the answer, the answer becomes unambiguous to B based upon B's information.
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You are being unclear.
Quartz... wrote:
but the solution space is not so its not what it looks like , if the solution space is 2 - 100 you will never get the other solution unanimously.
I think you meant "if the solution space is 2 - 100 you will never get the other solution by itself." Yet both the solutions occur 'by themselves' in the solutions given in that page, and I cannot see ANY difference in the solution spaces between your posting of the problem and the posting on that page.
and ALSO it contradicts the problem it self becuse if there are two solutions then how come the the two persons are sure about the anwser they will still have to decide between the two solutions right ?
Wrong. Each of them has a clue to the answer, and when A knows the answer, the answer becomes unambiguous to B based upon B's information.
There is a slight difference in the question itself The Problem given in that page is
A and B are positive integers greater than 1 ( there is no upper limit )
And the Problem here is
2 >= a,b ** >= 100**
I think thats the ony difference which filters out the second solution I am compilng the solution with a detailed explaination hope it will clearify it, sorry if i got you confused "Not everything that counts can be counted..." -Albert Einstein
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There is a slight difference in the question itself The Problem given in that page is
A and B are positive integers greater than 1 ( there is no upper limit )
And the Problem here is
2 >= a,b ** >= 100**
I think thats the ony difference which filters out the second solution I am compilng the solution with a detailed explaination hope it will clearify it, sorry if i got you confused "Not everything that counts can be counted..." -Albert Einstein
Now you are making no sense, and even contradicting your earlier posts. In the first post you said:
2 <= a,b <= 100
Now you say
2 >= a,b >= 100
I believe you meant the first one. And a and b in BOTH of the solutions on the page I showed are between 2 and 100. David