# Socks

sloppyb
Posers and Puzzles 19 Mar '10 00:14
1. 19 Mar '10 00:14
If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?
2. Kewpie
since 1-Feb-07
19 Mar '10 00:34
Five.
3. joe shmo
Strange Egg
19 Mar '10 01:00
Originally posted by sloppyb
If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?
6
4. AThousandYoung
iViva la Hispanidad!
19 Mar '10 03:40
5
5. 19 Mar '10 05:12
Five is enough.
6. joe shmo
Strange Egg
19 Mar '10 07:32
Originally posted by joe shmo
6
I must be wrong, can someone post the work?
7. AThousandYoung
iViva la Hispanidad!
19 Mar '10 07:51
Originally posted by joe shmo
I must be wrong, can someone post the work?
There are only four colors. Once you have one of each...then what?
8. forkedknight
Defend the Universe
19 Mar '10 18:26
Originally posted by AThousandYoung
There are only four colors. Once you have one of each...then what?
Pigeonhole principle...
9. 20 Mar '10 02:09
Shouldnt all this bollocks be covered in first year?
10. 20 Mar '10 09:20
Originally posted by neil67d
Shouldnt all this bollocks be covered in first year?
Not everyone here at RHP has started their first year (if I understand 'first year' correctly). But the pidgeon hole principle is a problem everyone can grasp. I use it myself to entertain guests in a party. Questions like stockings in a dark room where right and left doesn't matter, and gloves where it does matter, and such. Very appreciated.
11. 20 Mar '10 23:58

Feb 09. Then it was 10 socks.

Becuause of that thread I now buy all black socks and no other colour
so if I need socks in a power cut I can just take out two.
12. joe shmo
Strange Egg
22 Mar '10 01:092 edits
Originally posted by AThousandYoung
There are only four colors. Once you have one of each...then what?
Woops, I went right for the combinatorics ( which apparently I haven't the skill to use either).

Just out of curiosity can anyone show me how to come up with the correct answer using a combinatorial approach? I just think that I was way off logically, and managed to arrive in the realm of the correct solution by luck.
13. 22 Mar '10 08:44
first sock = colour a.
chance of second sock being colour a = 1/4

if not, second sock is colour b
chance of third sock being colour a or b = 1/2

if not, third sock is colour c
chance of fourth sock being a or b or c = 3/4

if not, fourth sock is colour d
chance of fifth sock being a or b or c or d = 1

So chance of getting a match by sock number n is:
N : Chance
1 : 0
2 : 1/4
3 : 1/4 + (1-1/4) * 1/2 = 5/8
4 : 5/8 + (1-5/8) * 3/4 = 29/32
5 : 29/32 + (1 - 29/32) * 1 = 1
14. forkedknight
Defend the Universe
22 Mar '10 15:59
Originally posted by iamatiger
first sock = colour a.
chance of second sock being colour a = 1/4

if not, second sock is colour b
chance of third sock being colour a or b = 1/2

if not, third sock is colour c
chance of fourth sock being a or b or c = 3/4

if not, fourth sock is colour d
chance of fifth sock being a or b or c or d = 1

So chance of getting a match by sock num ...[text shortened]...
3 : 1/4 + (1-1/4) * 1/2 = 5/8
4 : 5/8 + (1-5/8) * 3/4 = 29/32
5 : 29/32 + (1 - 29/32) * 1 = 1
Your math makes it seem like there are infinitely many socks in the drawer and they are evenly distributed between the 4 different color.

The problem does not reflect that.

There could be a million black socks, 19 red socks, 2 blue socks, and 1 green sock and the answer would still be 5.
15. AThousandYoung
iViva la Hispanidad!
22 Mar '10 21:26
Originally posted by joe shmo
Woops, I went right for the combinatorics ( which apparently I haven't the skill to use either).

Just out of curiosity can anyone show me how to come up with the correct answer using a combinatorial approach? I just think that I was way off logically, and managed to arrive in the realm of the correct solution by luck.
If your sock drawer has 6 black socks, 4 brown socks, 8 white socks, and 2 tan socks, how many socks would you have to pull out in the dark to be sure you had a matching pair?

There are 20 socks. Suppose you pull a white sock first. You cannot pull a white sock with certainty. We can model certainty as having atrocious luck. This means that you will now fail to pull a white sock 2nd.

Now we have 20 - 8 = 12 possible socks to pull without getting a pair. Suppose we pull a black sock. By the same reasoning, the third sock comes from a pool of only 6 possible "losing" socks. Say it's brown. The fourth must be the tan sock (we're talking worst possible luck here).

There are no colors left.

I don't know if that's just a long winded version of my previous post or not but I tried ðŸ™‚