Two integers, m and n, each between 2 and 100 inclusive, have been chosen. The product, mn, is given to mathematician P. The sum, m + n, is given to mathematician S. Their conversation is as follows:
S: "I know that you don't know the sum."
P: "Now I know the sum."
S: "And now I know your product."
What were the numbers?
2006-09-25 10:46:54 · 4 answers · asked by skins 2 in Science & Mathematics ➔ Mathematics
Since S is positive that P doesnt know the sum, the sum cannot possibly be the sum of 2 primes. If it could be the sum of 2 primes, then it could be possible for P to know the sum if he had a product that was the product of 2 primes. For example, if P had 21, then he would know the sum was 10, and that would contradict S. So the sum cannot be the sum of 2 primes ever. There are only a few numbers that can never be written as a sum of 2 primes. 11 is one such number but there are more. This should give you a good start
2006-09-25 10:53:24 · answer #1 · answered by Greg G 5 · 2⤊ 0⤋
4 and 13
2006-09-25 11:38:27 · answer #2 · answered by Jose M 1 · 1⤊ 0⤋
The answer is 4 and 13.
It's just about in the realms of my mathematical understanding but I can only say this after looking it up!
http://www.cs.utexas.edu/users/EWD/ewd06xx/EWD666.PDF
2006-09-25 11:23:34 · answer #3 · answered by Anonymous · 1⤊ 0⤋
gosh darn ding dang. i think i will just have a beer
2006-09-25 10:50:29 · answer #4 · answered by Billy T 6 · 0⤊ 2⤋