KC13 Posts: 2,556, Reputation: 99 Ultra Member #1 Jan 8, 2009, 04:40 PM
Riddle me that.
A wealthy man with a blind butler has overslept and is rushing to get ready for work. All of his socks (10 pair black, 10 pair white) are downstairs in the dryer. He summons his butler and tells him to get a pair of socks, either black or white. What is the fewest number of socks the butler must bring to assure he has a matching pair?
 JudyKayTee Posts: 46,503, Reputation: 4600 Uber Member #2 Jan 8, 2009, 05:41 PM
Originally Posted by KC13
A wealthy man with a blind butler has overslept and is rushing to get ready for work. All of his socks (10 pair black, 10 pair white) are downstairs in the dryer. He summons his butler and tells him to get a pair of socks, either black or white. What is the fewest number of socks the butler must bring to assure he has a matching pair?

The minimum would be 2. The maximum would be 3. You are not seeking a specific color matched pair so the butler would pull out one sock. It be either black or white.

The second sock could be black or white - if it matches the first, that's 2 socks.

If it does not match the third sock (either black or white) will match ONE of the first two - that's 3 socks.

?
 KC13 Posts: 2,556, Reputation: 99 Ultra Member #3 Jan 8, 2009, 05:59 PM
The correct answer is 3. Possible scenarios: 1 white/2 black, 1 black/2 white, 3 white, 3 black. A matching pair is assured with each scenario.
 JudyKayTee Posts: 46,503, Reputation: 4600 Uber Member #4 Jan 9, 2009, 06:42 AM
Originally Posted by KC13
The correct answer is 3. Possible scenarios: 1 white/2 black, 1 black/2 white, 3 white, 3 black. A matching pair is assured with each scenario.

I don't understand the answer of 3 - why isn't it possible that the butler would pull out two of the same color on the first two tries? I think you are overlooking that possibility and assuming that the first two socks out of the drawer will be different colors.

Why the assumption that the first two will be different colors and not the same color?
 Capuchin Posts: 5,255, Reputation: 656 Uber Member #5 Jan 9, 2009, 07:57 AM
Originally Posted by JudyKayTee
I don't understand the answer of 3 - why isn't it possible that the butler would pull out two of the same color on the first two tries? I think you are overlooking that possibility and assuming that the first two socks out of the drawer will be different colors.

Why the assumption that the first two will be different colors and not the same color?
He's looking for the minimum number to assure a matching pair. The answer is 3.
 JudyKayTee Posts: 46,503, Reputation: 4600 Uber Member #6 Jan 9, 2009, 07:58 AM
Originally Posted by Capuchin
He's looking for the minimum number to assure a matching pair. The answer is 3.

OK, got it.
 ISneezeFunny Posts: 4,175, Reputation: 821 Ultra Member #7 Jan 9, 2009, 08:04 AM

... I'm kind of hoping the butler grabs one sock and a wooden spoon...
 JudyKayTee Posts: 46,503, Reputation: 4600 Uber Member #8 Jan 9, 2009, 08:51 AM
Originally Posted by ISneezeFunny
...I'm kinda hoping the butler grabs one sock and a wooden spoon...

I figure the butler will show up with two socks, maybe matching, maybe not - the blind guy can't tell anyway and everyone will be too polite to mention it.

So - I'm back to an answer of two.
 KC13 Posts: 2,556, Reputation: 99 Ultra Member #9 Jan 9, 2009, 03:34 PM
Originally Posted by Capuchin
He's looking for the minimum number to assure a matching pair. The answer is 3.
Thank you.

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