A puzzle about sum and product
Inviato: 26/11/2012, 18:02
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https://www.matematicamente.it:443/forum/viewtopic.php?f=25&t=106352
We pick two numbers \(a\) and \(b\), so that \(a\geq b\) and both numbers are within the range \([2,99]\). We give Mr.P the product \(a\cdot b\) and give Mr.S the sum \(a+b\).
The following dialog takes place:
Mr.P: I don't know the numbers
Mr.S: I knew you didn't know. I don't know either.
Mr.P: Now I know the numbers
Mr.S: Now I know them too
Can we find the numbers \(a\) and \(b\)?