Quote:
Originally posted by anabolik
if you solve this, please email me at anabolikfrolik@yahoo.com..............
a man comes up with two numbers between 1 and 99 (meaning not 1 or 99 but from 2 to 98). The sum of these two numbers is under 99. He tells one person the sum of these numbers and another person the product of these numbers. The person with the product comes up to the person with the sum and says "i don't know the two numbers". The person with the sum replies with "i know that you don't know the two numbers". Immediately, the man with the product says "now i know the two numbers" and the man with the sum says "now i know the two numbers too". What are the two numbers? There is no word play involved.. it is a real problem with a real answer. Feel free to find the answer any way possible. Thanks! my email is anabolikfrolik@yahoo.com
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Let's call the product p, and the guy who has it P,
and the sum s and the guy who has it S.
For P to know the answer, p=axb
where a and b are primes ( not necessariliy distinct).
So if P doesn't know the answer, then a and b are not obviously primes.
For S to know that P doesn't know the answer, S must know that
no primes a and b exists such that s=a+b
The list of primes from from 2 to 98 inclusive are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
using the list we can calculate all the sums obtainable by adding two primes. There are only few sums not obtainable by that method. They are:
27 41 51 57 71 83 87 93 97
Now, we know that the value can't be a prime for it to be a product too. So we eliminate the primes, and are left with
27 57 87
However, some of these are the products of two primes. If they were, then P would've known the answer. So we eliminate them too. And we are left with just
27
So 27 can be obtained only by 9 x 3
so our numbers are
9 and 3
This is the only method I can think of. Maybe there is an easier method. Or am I totally wrong?
AmigoRo