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10 replies to this topic

### #1 Pickett

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Posted 19 February 2009 - 06:35 PM

I couldn't find this one on the site...so I figured I'd post it...if it has already been done, I apologize...

There was once a king who wanted to determine who the smartest person in the land was (funny how that seems to happen a lot in these forums). After a bunch of tests, it was down to two men (P and S), who claimed to be "perfect" logicians (meaning there was never any flaw in their logic).

The king then told them their final test:

"I am thinking of two different numbers greater than 1, whose sum is less than 100. I will tell P the product of my two numbers, and I will tell S the sum of the two numbers," the kind stated.

The king whispers in P's ear the product of his two numbers, and whispers to S the sum of the two numbers...The following is the conversation that the logicians had:

P: I don't know the two numbers...
S: I know you don't
P: Ah...now I know them...
S: So do I

Together, both men then stated the two numbers to the king, and he stared in disbelief...

What were the two numbers?

(NOTE: I actually wrote a program to solve this puzzle...however, I know it can be done without the use of any computer...)
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### #2 Prime

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Posted 19 February 2009 - 08:35 PM

A more difficult variation of same puzzle had been posted awhile ago.
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Past prime, actually.

### #3 Prime

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Posted 19 February 2009 - 09:20 PM

As for this variation the answer could be:

To find whether this is the only possible solution, you'd still save a lot of time by writing a computer program. I suspect, there are other solutions.
As far as puzzles go, this variation is more fair than the one posted before. Because solving the other one without a computer program was not a feasible task. I would change the question of the puzzle "What could be the numbers?"
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Past prime, actually.

### #4 Pickett

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Posted 19 February 2009 - 09:31 PM

As for this variation the answer could be:

To find whether this is the only possible solution, you'd still save a lot of time by writing a computer program. I suspect, there are other solutions.
As far as puzzles go, this variation is more fair than the one posted before. Because solving the other one without a computer program was not a feasible task. I would change the question of the puzzle "What could be the numbers?"

After looking at the other problem posted, I'm not sure if this one is actually any easier...in fact I could solve the other one easier than this one (however that could just be the way I think)...

Second, this is not at all what I got for my answer...I'm confused as to how you made the statement that P has two choices and why those were the only 2 choices P had. Unless I have misstated the problem, you over-simplified it...maybe if you walk through how you got the answer...because from what I have found there is only one possible answer to this problem, and it is not the one that you stated...
Spoiler for Starters

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### #5 voltage

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Posted 19 February 2009 - 09:58 PM

As for this variation the answer could be:

Actually that's not an answer. Here's why:

the key is in the second statement: I know that you do not know. That means that every possible combination of numbers that add up to 31 (i.e. 2+29, 3+28, 4+27...) when multiplied together must have multiple factors. 2*29 = 58 has only 1 possible factorization. Therefore, if S is given 31, he can't say "I know you don't know"
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### #6 Prime

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Posted 19 February 2009 - 10:08 PM

After looking at the other problem posted, I'm not sure if this one is actually any easier...in fact I could solve the other one easier than this one (however that could just be the way I think)...

Second, this is not at all what I got for my answer...I'm confused as to how you made the statement that P has two choices and why those were the only 2 choices P had. Unless I have misstated the problem, you over-simplified it...maybe if you walk through how you got the answer...because from what I have found there is only one possible answer to this problem, and it is not the one that you stated...

Spoiler for Starters

Sorry, my mistake. I didn't pay due attention to the statement of the problem. I just saw the names P and S, and assumed this problem was the same. (The other puzzle had two two-digit numbers.) So scratch my previous posts.

However, I don't see, why product couldn't be a 4th power of a prime. Say, 81 could be 9*9, or it could be 3*27.

Edited by Prime, 19 February 2009 - 10:10 PM.

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Past prime, actually.

### #7 Pickett

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Posted 19 February 2009 - 10:10 PM

Sorry, my mistake. I didn't pay due attention to the statement of the problem. I just saw the names P and S, and assumed this problem was the same. (The other puzzle had two two-digit numbers.) So scratch my previous posts.

However, I don't see, why product couldn't be a 4th power of a prime. Say, 81 could be 9*9, or it could be 3*27.

can't be 9*9 since it says they are distinct numbers...so that means it could only be 3 * 27...and therefore he would know the answer just by that
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### #8 Prime

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Posted 19 February 2009 - 10:47 PM

Here the first statement by S "I know, you don't" gives me problems. (I assume, by that he meant that he knew that P couldn't tell the numbers without him saying so.)
Spoiler for is it?

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Past prime, actually.

### #9 Prof. Templeton

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Posted 19 February 2009 - 11:07 PM

Spoiler for I'm sure they are

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### #10 Pickett

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Posted 19 February 2009 - 11:27 PM

Spoiler for I'm sure they are

Correct...It's a great riddle...I'm assuming you figured out how to get the answer and are leaving that up for everyone else to figure out

And yes, that is the only answer to the puzzle...
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