Posers and Puzzles

Posers and Puzzles

  1. Joined
    31 Jan '09
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    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. SubscriberKewpie
    since 1-Feb-07
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    19 Mar '10 00:34
    Five.
  3. Subscriberjoe shmo
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    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. SubscriberAThousandYoung
    iViva la Hispanidad!
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    19 Mar '10 03:40
    5
  5. Joined
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    19 Mar '10 05:12
    Five is enough.
  6. Subscriberjoe shmo
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    19 Mar '10 07:32
    Originally posted by joe shmo
    6
    I must be wrong, can someone post the work?
  7. SubscriberAThousandYoung
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    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. Standard memberforkedknight
    Defend the Universe
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    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. Joined
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    20 Mar '10 02:09
    Shouldnt all this bollocks be covered in first year?
  10. Joined
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    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. e4
    Joined
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    20 Mar '10 23:58
    Thread 107865

    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. Subscriberjoe shmo
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    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. Joined
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    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. Standard memberforkedknight
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    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. SubscriberAThousandYoung
    iViva la Hispanidad!
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    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 🙂
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