Freethought & Rationalism Archive

Lobstrosity · 05-09-2003, 01:42 AM

Two mathematicians, Sam and Polly, are walking down the street when they encounter a strange man (let's call him Nick). This man tells the two that he is thinking of two integers, each of which is greater than two but less than 50. He leans over and whispers to Sam the sum of the two numbers. He then leans over and whispers to Polly the product of the two numbers. The following conversation between Sam and Polly then ensues:

Sam: "I know that you do not know what numbers Nick is thinking of."

Polly: "Ah, but now I do know what numbers Nick is thinking of."

Sam: "And now so do I."

The problem for you: what are the numbers Nick is thinking of?

Jabu Khan · 05-09-2003, 02:49 AM

49 and 48?

Jesse · 05-09-2003, 04:46 AM

Quote:

Originally posted by Jabu Khan
49 and 48?

Can't be. Then Sam's sum would be 97, and there's only one way to get 97 using two integers smaller than 50: 49+48. So, he would know the two numbers are 49 and 48 from the start, so he'd therefore also know that Polly's product is 2352, and there's only one way to get that product using two numbers under 50: 49 * 48. So, he'd know that Polly should know the two numbers from the start as well.

BTW, you can tell there's no other way to factor 2352 into two numbers between 3 and 50 by looking at its prime factors--7*7*3*2*2*2*2. If you divide those into two groups, the only way to keep both groups under 50 is (7*7)*(3*2*2*2*2).

johngalt · 05-09-2003, 07:17 AM

47 and 48.

Sr. Zonules · 05-09-2003, 07:42 AM

it can't be 47 and 48 (nor 46 and 49) because they also have unique factors.

47 + 48 = 46 + 49 (= 95)

47 * 48 = 2256 = 2^4 * 3 *47
46 * 49 = 2254 = 2 * 7^2 * 23

-Z

Sr. Zonules · 05-09-2003, 07:43 AM

The numbers have to be different, correct? I'll assume so for now...

-Z

Soyin Milka · 05-09-2003, 10:18 AM

Hm.

4 and 13?

Soyin

Majestyk · 05-09-2003, 11:27 AM

A > 2, < 50
B > 2, < 50

A + B = S = not P

AB = P = not S

A = S � B = not P

A = P/B = not S

Am I even approaching this correctly?

Majestyk · 05-09-2003, 11:57 AM

12, 25 as in 12/25 or December, 25th. x-mas. Nick is St. Nicholas aka Santa Claus!

Jesse · 05-09-2003, 12:38 PM

Quote:

Originally posted by Soyin Milka
Hm.

4 and 13?

Soyin

Then the product would be 52, which broken down into its prime factors is 2*2*13. There's only one way to group that into two numbers that are both larger than 2: (2*2) and 13. So Polly would know the two numbers were 4 and 13 right away.

05-09-2003, 01:42 AM	#1
Lobstrosity Senior Member Join Date: Feb 2003 Location: San Diego, California Posts: 719	Yet another entertaining math problem Two mathematicians, Sam and Polly, are walking down the street when they encounter a strange man (let's call him Nick). This man tells the two that he is thinking of two integers, each of which is greater than two but less than 50. He leans over and whispers to Sam the sum of the two numbers. He then leans over and whispers to Polly the product of the two numbers. The following conversation between Sam and Polly then ensues: Sam: "I know that you do not know what numbers Nick is thinking of." Polly: "Ah, but now I do know what numbers Nick is thinking of." Sam: "And now so do I." The problem for you: what are the numbers Nick is thinking of?

05-09-2003, 07:42 AM	#5
Sr. Zonules Junior Member Join Date: Oct 2002 Location: N 47� 11� 14�, W 122� 10� 08� Posts: 82	a start... it can't be 47 and 48 (nor 46 and 49) because they also have unique factors. 47 + 48 = 46 + 49 (= 95) 47 * 48 = 2256 = 2^4 * 3 47 46 49 = 2254 = 2 * 7^2 * 23 -Z

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05-09-2003, 02:49 AM	#2
Jabu Khan Veteran Member Join Date: Apr 2003 Location: the impenetrable fortress of the bubbleheads Posts: 1,308	49 and 48?

05-09-2003, 07:17 AM	#4
johngalt Regular Member Join Date: Apr 2003 Location: Chicago, IL Posts: 204	47 and 48.

05-09-2003, 07:43 AM	#6
Sr. Zonules Junior Member Join Date: Oct 2002 Location: N 47� 11� 14�, W 122� 10� 08� Posts: 82	The numbers have to be different, correct? I'll assume so for now... -Z

05-09-2003, 10:18 AM	#7
Soyin Milka Regular Member Join Date: Mar 2003 Location: Absurdistan Posts: 299	Hm. 4 and 13? Soyin

05-09-2003, 11:27 AM	#8
Majestyk Veteran Member Join Date: Mar 2003 Location: Northeast Ohio Posts: 2,846	A > 2, < 50 B > 2, < 50 A + B = S = not P AB = P = not S A = S � B = not P A = P/B = not S Am I even approaching this correctly?

05-09-2003, 11:57 AM	#9
Majestyk Veteran Member Join Date: Mar 2003 Location: Northeast Ohio Posts: 2,846	12, 25 as in 12/25 or December, 25th. x-mas. Nick is St. Nicholas aka Santa Claus!

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