Yes, and that's all they know at the beginning!Quote:
Originally posted by SeventhStar
s know the sum and p know the product right?
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Yes, and that's all they know at the beginning!Quote:
Originally posted by SeventhStar
s know the sum and p know the product right?
A=(SUM+SQRT(SUM*SUM-4*PROD))/2
B=(SUM-SQRT(SUM*SUM-4*PROD))/2
This means we already have three 6's. I thought I wouldn't have 660 to go. :D :p :p
1. Is this already the complete answer?Quote:
A=(SUM+SQRT(SUM*SUM-4*PROD))/2
B=(SUM-SQRT(SUM*SUM-4*PROD))/2
2. If so, why? :confused:
It is easy to test:
A+B=SUM
A*B=PROD
OK, but the preceding dialogue between P and S suggests that by knowing that S knew that P can't find the numbers, P can figure them out (the actual values!), and with this knowledge, S finds them too. In my opinion, it must have something to do with prime factorials...Quote:
Originally posted by Doctor Luz
It is easy to test:
A+B=SUM
A*B=PROD
You seem to be missing that P and S know the product and the sum *respectively*. IMHO, this means that P knows *only* the product and S *only* the sum, and these values are never communicated between S and P.
You say S knows A and B right? If sum and product are never comunicated I don't know how S can know A and B only knowing A+B. There are infinite posibilities except if one number is 0.
in this case A=sum b=0; PROD=0
@Elrond: Are A and B allowed to be equal?
Quote:
Originally posted by Doctor Luz
You say S knows A and B right? If sum and product are never comunicated I don't know how S can know A and B only knowing A+B. There are infinite posibilities except if one number is 0.
in this case A=sum b=0; PROD=0
No, S knows A+B, not A and B.Quote:
You say S knows A and B right?
No, because A and B are between 2 and 100.Quote:
There are infinite posibilities except if one number is 0.
S not only knows A+B, he equally knows that P can't find the numbers knowing only the product.Quote:
I don't know how S can know A and B only knowing A+B.
NO!!!!Quote:
Originally posted by Doctor Luz
You say S knows A and B right? If sum and product are never comunicated I don't know how S can know A and B only knowing A+B. There are infinite posibilities except if one number is 0.
in this case A=sum b=0; PROD=0
S only knows the result of A+B, he does not know A, B, or A*B.
P only knows the result of A*B, he does not know A, B or A+B.
The only additional thing each of them know if that A and B are between 2 and 100. It means that if A+B = 128, S know that it cannot be something like 112+16, and the if A*B = 256, P knows that it cannot be 128*2.
Then they don't speak any additional word except the ones I have told you.
As far as I know, there's no rule about A and B being equal or different.
You are right, I did not read those details.
I should read more carefully. Sorry
Elrond, this is a hard one! :eek:
Is it OK to think aloud? Just to know if the approach is correct, or if it's somethig completely different.
Yes, it's OK to think aloud. The only risk is that some one takes your ideas to get the correct answer. ;)
I'll face this risk. Let's see:Quote:
Originally posted by Elrond
Yes, it's OK to think aloud. The only risk is that some one takes your ideas to get the correct answer. ;)
1. P states that he can't find the numbers. This means that the A and B cannot be prime, as the solution would otherwise be obvious to P.
2. S states that he knew that. This *could* mean to P (but need not) that S knew that the numbers cannot be prime. He could have deduced that by the fact that the sum is odd (Goldbach's conjecture states that every even integer >= 4 can be written as the sum of two primes. Although it has not generally been proven, it has been proven for numbers < 4*10^14 AFAIK).
3. Assuming the sum is odd, this means that either A or B is odd and the other is even.
At this point, I'm stuck... I feel that there can be made more deductions from the fact that P can't find A and B (what about squares?), but I'm still missing something.
It only means that not both numbers at the same time can be prime.Quote:
Originally posted by gstercken
1. P states that he can't find the numbers. This means that the A and B cannot be prime, as the solution would otherwise be obvious to P.