March 3–March 9, 2009

Problem

You have a plate of spaghetti and carry out the following procedure: Pick up two free ends of spaghetti noodles (they may/may not be ends of the same noodle) and tie them together. Repeat until all the ends have been tied. In the end, you'll have loops made of spaghetti.

  1. If there were N noodles to begin with, what is the expected number of loops?
  2. What's the smallest number of noodles needed to expect more than 5 loops?

Solution

here

List of solvers

Jacob Lewis, Koopa Koo, Dustin Moody (graduate); David Kaplan, Gary M. Raymond, Chaitanya Rachabattuni, Steve Wilmarth, Mike Goodman, Justin Shih, Luan Nguyen, Zoheb Vacheri, Roman Holenstein, Lloyd Sakazaki (outside).

Gary Raymond wins the prize!