1. In your face
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    13 Sep '05 23:36
    A chauffer has 5 pairs of white gloves, 3 pairs of black gloves and 2 pairs of brown gloves in his draw. Without looking, how many gloves does he need to pull out of the draw to be sure he makes a complete pair?

    ANd another one...

    How many cards can be pulled out of a complete set of 52 playing cards, without having a full house combination?
  2. Standard memberPBE6
    Bananarama
    False berry
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    14 Sep '05 00:20
    Originally posted by jimslyp69
    A chauffer has 5 pairs of white gloves, 3 pairs of black gloves and 2 pairs of brown gloves in his draw. Without looking, how many gloves does he need to pull out of the draw to be sure he makes a complete pair?

    ANd another one...

    How many cards can be pulled out of a complete set of 52 playing cards, without having a full house combination?
    OK:

    (1) The chauffeur can pull out 5 lefty white gloves, 3 lefty black gloves and 2 lefty brown gloves. After that, the next glove will complete some pair, so the chauffer needs to pull out 5+3+2+1 = 11 gloves to be sure.

    (2) A full house, consisting of one pair and one three of a kind, can be put off the longest by drawing a pair from each rank. After that, any card will complete some three of a kind making a full house. So the most cards that can be drawn without making a full house is 13*2 = 26 cards. The 27th card will make the full house.

    Interesting questions. These are examples of problems that can be solved using the pigeonhole principle, a simple but powerful mathematical tool.
  3. Standard memberBowmann
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    14 Sep '05 18:29
    In the chauffeur's sock drawer, he has a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks...
  4. Earth Prime
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    14 Sep '05 23:24
    Originally posted by Bowmann
    In the chauffeur's sock drawer, he has a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks...
    4
  5. Subscribersonhouse
    Fast and Curious
    slatington, pa, usa
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    01 Oct '05 05:26
    Originally posted by PBE6
    OK:

    (1) The chauffeur can pull out 5 lefty white gloves, 3 lefty black gloves and 2 lefty brown gloves. After that, the next glove will complete some pair, so the chauffer needs to pull out 5+3+2+1 = 11 gloves to be sure.

    (2) A full house, consisting of one pair and one three of a kind, can be put off the longest by drawing a pair from each rank. Afte ...[text shortened]... lems that can be solved using the pigeonhole principle, a simple but powerful mathematical tool.
    Please expand on the pigeonhole principle, never heard of it.
  6. Standard memberBowmann
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    19 Oct '05 15:12
    Originally posted by sonhouse
    Please expand on the pigeonhole principle, never heard of it.
    Don't you get Google in Slatington?
  7. Standard memberroyalchicken
    CHAOS GHOST!!!
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    19 Oct '05 17:181 edit
    Originally posted by sonhouse
    Please expand on the pigeonhole principle, never heard of it.
    Given two finite sets S and T, f: S->T is bijective if and only if card S = card T. In particular, if card T < card S, there must exist some t in T such that t = f(s1) and f(s2) for distinct s1, s2 in S.

    A shavixmirian example: The average person has, I would guess, on the order of 10^5 pubes, and certainly nobody has more than 10^6 (I should hope). Since there are about 7*10^9 people in the world, the pigeonhole principle guarantees that there exist two people with the same number of pubes (this is an example of what's known as 'fuzzy logic' 😉).
  8. Standard memberPBE6
    Bananarama
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    19 Oct '05 18:04
    Originally posted by royalchicken
    A shavixmirian example: The average person has, I would guess, on the order of 10^5 pubes, and certainly nobody has more than 10^6 (I should hope). Since there are about 7*10^9 people in the world, the pigeonhole principle guarantees that there exist two people with the same number of pubes (this is an example of what's known as 'fuzzy logic' 😉).
    That's funny, I thought it was called the Crab Nebula. 😕
  9. Subscribersonhouse
    Fast and Curious
    slatington, pa, usa
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    19 Oct '05 20:17
    Originally posted by Bowmann
    Don't you get Google in Slatington?
    too far out in the country, that plus terminal laziness.....
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