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        riddles >> medium >> Re: Variant of "Product & Sum" puzzl
        
(Message started by: towr on Jan 7^th, 2008, 11:47am)

Title: Re: Variant of "Product & Sum" puzzl
Post by towr on Jan 7^th, 2008, 11:47am

(second attempt)

[hide]Let's call person 1 Simon, and person 2 Paul
Simon has the sum=136, and Paul the product=135

Simon essentially says that the sum is not a prime+1 (because otherwise Paul might know the sum if the product he was given was a prime)

Paul know how he can factor his number and what sums this would mean for Simon
product sum
1*135 -> 136=135+1
5*27 -> 32=31+1
15*9 -> 24=23+1
45*3 -> 48=47+1
23, 31 and 47 are primes; so if Simon had any of the last three sums, he couldn't be certain Paul didn't know his number. As Simon is certain, those three options are excluded. And Paul is left with just the choice 1 and 135 for a,b and thus knows the sum as well.[/hide]

Title: Re: Variant of "Product & Sum" puzzl
Post by Ghost Sniper on Jan 8^th, 2008, 10:12am

Note that it could be the sum that is constantly equal to 136.

From what I get, the product of the 2 numbers is [hide]655[/hide], with a and b both primes, [hide]131 and 5[/hide]. There might be other answers, but I don't have time to find the answers. I gotta get back to class. :P

Title: Re: Variant of "Product & Sum" puzzl
Post by towr on Jan 8^th, 2008, 3:19pm

on 01/08/08 at 10:12:25, Ghost Sniper wrote:

Note that it could be the sum that is constantly equal to 136.

?! I'm not sure what you mean by this..

Quote:

From what I get, the product of the 2 numbers is [hide]655[/hide], with a and b both primes, [hide]131 and 5[/hide]. There might be other answers, but I don't have time to find the answers. I gotta get back to class. :P

If the product were [hide]655[/hide], the sum might be either 136 or 656; so the second person already knows that the first person knows that the second person cannot know the sum. So the first person saying this does not yield him any information to deduce the sum with.