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Posers and Puzzles

Posers and Puzzles

  1. 07 Jun '06 21:05
    My rather untidy friend has 100 pieces of string, which are tangled
    into a ball so that each of the 200 ends are protruding from the
    surface. My friend picks one of the 200 ends at random, and attaches
    it randomly to one of the 199 remaining ends. After this he picks
    another end at random, and then attaches this randomly to one of the
    remaining 197 ends. Continuing in this way, he finally joins all
    200 of the ends up, leaving a number of loops of string. On
    average, how many loops should he expect to obtain?
  2. Subscriber BigDoggProblem
    The Advanced Mind
    07 Jun '06 21:49
    Originally posted by SPMars
    My rather untidy friend has 100 pieces of string, which are tangled
    into a ball so that each of the 200 ends are protruding from the
    surface. My friend picks one of the 200 ends at random, and attaches
    it randomly to one of the 199 remaining ends. After this he picks
    another end at random, and then attaches this randomly to one of the
    remaining 197 end ...[text shortened]... p, leaving a number of loops of string. On
    average, how many loops should he expect to obtain?
    Not as many as a tidy person would.
  3. 07 Jun '06 22:31
    Originally posted by SPMars
    My rather untidy friend has 100 pieces of string, which are tangled
    into a ball so that each of the 200 ends are protruding from the
    surface. My friend picks one of the 200 ends at random, and attaches
    it randomly to one of the 199 remaining ends. After this he picks
    another end at random, and then attaches this randomly to one of the
    remaining 197 end ...[text shortened]... p, leaving a number of loops of string. On
    average, how many loops should he expect to obtain?
    3.284?
  4. 08 Jun '06 10:08
    Very good!

    The exact answer is

    1 + 1/3 + 1/5 + 1/7 + ... 1/197 + 1/199.
  5. 15 Jun '06 06:51
    i'm not sure if you took this into account with the average (or if it makes a difference) but what if you had five strings tied in a row which eventually formed one big loop
  6. Standard member XanthosNZ
    Cancerous Bus Crash
    15 Jun '06 07:34
    Originally posted by Gburg2006
    i'm not sure if you took this into account with the average (or if it makes a difference) but what if you had five strings tied in a row which eventually formed one big loop
    Of course they took that into account that's the whole point of the problem.