There are 100 insulated wires running through a pipe. At each end of the pipe, the wires are shorted together in randomly choosen pairs; the pairs independently choosen at each end. Since no open ends are left over, these hundred wires will form one or more independent closed circuits.

Calculate the average number of such circuits.



A cute puzzle:

You are given twelve 3″ x 9″ paper envelopes and sixty paperclips. Rearrange the material so that each envelope contains a distinct number of paperclips. It is not allowed to cut the paperclips or envelopes.