139 and 38 ?
There was a king.....
He chose 2 nos lying between 10 and 40 .
He told one mathematician the product of these 2 numbers....
He told the other mathematician the sum of these 2 numbers....
The mathematicians where not allowed to talk two each other thro' voice or writing or any kind of signals......
He asked the 1st mathematician the 2 nos........... he was unable to tell
He asked the 2nd mathematician the 2 nos........... he was also unable to tell......
Then again he asked the 1st mathematician the 2 nos........... he said i know it.....
Then again he asked the 2 nd mathematician the 2 nos........... he said i know it too.........
what are the 2 nos.......
here is one hint :) ....... sorry i was out of town so could not reply :
If the limits would have been 0 to 10 then answer is 2 and 6. The smallest number with two permissible product decompositions is 12=2*6=3*4. If the second mathematician had 7=3+4, he would have to be deciding between 3,4 and 2,5. Since 10=2*5 has only one product decomposition, it is out, so the second mathematician would have known the answer (3,4) after the first mathematician answered no the first time. Therefore it could not have been 7=3+4. If the numbers were larger, the negative answer of the second mathematician would not have given enough information to the first.
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5 Answers
1Now the sum should be such that only 1 possible pair will satisfy it in 10<x,y<40.
Also the product should be such that only x*y = y*x = the product.
38 and 39 satisfy both the conditions.
( I don't know why they weren't able to answer the first time )
11But you can always form a quadratic equation whose roots lie between
10 and 40. For example,
(x-20) (x-30) = x2 -50x + 600
has roots 20 and 30 as roots, both between 10 and 40.
You just need two numbers between 10 and 40 and you will have a sum and a product for those numbers, isn't it?
1The mathematician who knows the product doesn't know the sum and the one who knows the sum doesn't know the product.