Another entry for the MOCAthalon here, this one for the category "Rube Goldberg Machine". I have always been fascinated with Great Ball Contraption modules and Mr. Goldberg's fanciful inventions, so this was loads of fun to do. I really enjoyed the challenges and engineering opportunities that this gave me, and I look forward to doing something like this again. Judges, this is probably my favorite category, so my hat is off to whoever thought of this one.
Thanks all for the support and comments. Be sure to watch the videos (especially the Youtube one, for 1080p HD!) so you can see how it works. I shall lay out a detailed synthesis below though.
Have a great Easter!
SOLI DEO GLORIA!
Chain of Events
 I press start button to trigger the first instance.  The start button retracts a hydraulic.  The retracted hydraulic allows a cart to roll down a ramp.  The cart has a magnet on top which connects to a beam.  The momentum of the cart spins the beam around.  The spinning of the releases a tightly wound rope that unwinds itself.  The unwinding rope eventually hits the blue ball.  The blue ball rolls down the ramp until it hits an arm.  The arm carries the blue ball forward onto the next ramp, while also hitting another smaller blue ball underneath of it. [10a] The big blue ball continues to roll down a series of ramps. [10b] The little blue ball rolls down the track until it falls into a bucket. [11a] The big blue ball hits a pressure pad that releases a trebuchet arm. [11b] The little ball that is inside the bucket of the trebuchet is released when the big ball hits the pad, and is careened into the air.  The ball is caught on a ramp.  The ball comes into contact with a sensitive beam that falls.  The falling of the beam releases a string that is connected to a guillotine-like release mechanism.  The "blade" touches a ball which sends it rolling down a ramp.  The ball touches a pin.  The pin releases a magnet that is attached to a pendulum.  On the opposite amplitude of the pendulum's swing, the magnet attaches to another magnet.  The magnet is pulled due to the increasing kinetic energy of the pendulum's backswing.  The pulling of the magnet pulls a pin.  The pulling of the pin releases a hammer.  The hammer applies weight to a touch sensor.  The touch sensor connects an electric current from a 9v battery to a motor.  The motor spins gears.  The gears hit a plate with teeth in it.  The plate is forced forward, forcing a stick of gum out of a chamber.  Nom nom nom!
The use of color here - industrial yellow and black, contrasted with the bright blue balls, is fantastic. And, 23 (I think) steps to dispense gum! That's simply amazing. Hopefully you'll keep this one for Lego conventions or some other displays. This cannot get less than 5 points from me.
RUBE GOLDBERG LIVES!!!
I was always fascinated by the Rube Goldberg designs as a kid. Hence MOUSE TRAP became my favorite game! This brings back memories to us "old timers" and introduces the concept to the younger MOCpagers!