Loops of Spaghetti

You are given a plate of spaghetti and told to do the following: Pick up one end of a spaghetti noodle and tie it to another end of a noodle. Continue to do this until all the ends have been tied together. If there were originally N pieces of spaghetti, what is the expected number of loops of spaghetti you would form? A loop may consist of any number of pieces of spaghetti tied together, and the loops could be linked to one another.

An "expected number" is the average number if the procedure were to be carried out many times.

Source: Stanford EE Ph.D. qualifying exam study questions.

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