ball

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?

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?

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?

Very good!

The exact answer is

1 + 1/3 + 1/5 + 1/7 + ... 1/197 + 1/199.

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

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