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Topic: Re: Variant of "Product & Sum" puzzl (Read 567 times) |
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towr
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Re: Variant of "Product & Sum" puzzl
« on: Jan 7th, 2008, 11:47am » |
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(second attempt)
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.
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| « Last Edit: Jan 7th, 2008, 11:53am by towr » |
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Ghost Sniper
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Re: Variant of "Product & Sum" puzzl
« Reply #1 on: Jan 8th, 2008, 10:12am » |
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Note that it could be the sum that is constantly equal to 136.
From what I get, the product of the 2 numbers is 655, with a and b both primes, 131 and 5. There might be other answers, but I don't have time to find the answers. I gotta get back to class. 
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towr
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Re: Variant of "Product & Sum" puzzl
« Reply #2 on: Jan 8th, 2008, 3:19pm » |
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on Jan 8th, 2008, 10:12am, Ghost Sniper wrote:| Note that it could be the sum that is constantly equal to 136. |
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?! I'm not sure what you mean by this..
Quote:| From what I get, the product of the 2 numbers is 655, with a and b both primes, 131 and 5. There might be other answers, but I don't have time to find the answers. I gotta get back to class. |
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If the product were 655, 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.
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| « Last Edit: Jan 8th, 2008, 3:22pm by towr » |
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