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Need help picking socks

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Senior | Next Rank: 100 Posts
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by TryHarder » Thu Jun 04, 2009 12:24 pm
Here is the question, I think the author missed to provide some details. Want to find out what you guys think.

A drawer contains red socks, black socks, and white socks. What is the least number of socks that must randomly be taken out of the drawer to be sure of having four pairs of socks?
(A pair is two socks of the same color)
A. 8
B. 10
C. 12
D. 14
E. 16

Now without knowing how many of each type there are how can one proceed?
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by agoyal2 » Fri Jun 05, 2009 10:30 am
IMO B.

Keep drawing socks while trying to avoid picking a pair in each draw. At some point you will have to pick a sock that completes a pair. Continue till you have 4 pairs. I could come up with the following.

possible sequence(s):
R, B, W, R, B, W, R, B, W, R [4 pairs]
R, B, W, R, R, R, R, R, R, R [ 4 pairs]

OA Pls?!?
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by Osirus@VeritasPrep » Fri Jun 05, 2009 10:41 am
I can't explain the theory or correct way to do it, but I would imagine that the answer has to be 12.

Red Red Red Red Red Red Red Red Red Red Red Red

Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue

White White White White White White White White White White White White

the longest way to get to four pairs is if you keep drawing a different color sock. If you do this just cross off one of each color until you have 4 pairs and you would have drawn 12 different socks.
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