Mathematicians - Treat for the weekend / might drive you crazy
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The numbers are 3 and 4. Explanation: B is told the sum: 7. He knows that only 2 different pairs of numbers greater than 2 can give a sum of 7 : 3+4 and 2+5. Therefore:
Quartz... wrote:
1=> B: I cannot determine a, b.
A is told the product: 12. He knows that there are just 2 different pairs of numbers greater than 2 which give this result: 2*6 and 3*4. So:
Quartz... wrote:
2=> A: I cannot determine a, b
Now, B knows 2 things. He knows A's ambiguity if the numbers are 3 and 4. And he knows that if they were 2 and 5 (as B considered) then A wouldn't have an ambiguity; these 2 numbers would generate a unique product of 10. Facing A's ambiguity:
Quartz... wrote:
3=> B: I already knew that.
A perceives that B solved it's own ambiguity and the only possibility of this happening is that the numbers are 3 and 4. If they were 2 and 6 as he considered the sum would be 8, wich would give 3 diferent possibilities to B (4+4, 2+6, 3+5). So:
Quartz... wrote:
4=> A: In that case, I now know them
And B already knew the answer. Makes sense? Did I preserve my sanity? Rui A. Rebelo I don't smoke, don't gamble, don't sniff, don't drink and don't womanize. My only defect is that I lie just a little bit, sometimes. Tim Maia (brazilian pop singer)
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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
6 and 7 The answer to everything. :-) Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
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6 and 7 The answer to everything. :-) Regardz Colin J Davies The most LinkedIn CPian (that I know of anyhow) :-)
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The answer to everything but this one :) No explanation ??? The solution is so simple that it will explain everything and everything fits into the picture perfectly like a jigsaw puzzle "Not everything that counts can be counted..." -Albert Einstein
explanations are for sissys 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
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