The Monty Hall puzzle:
   
   Monty Hall hosts a TV game show in which contestants try to win cars.
   Before each contestant plays, a car is put behind one of three closed
   doors.  The other two doors have goats behind them.  The contestant
   gets to choose one of the three doors.  Monty Hall then opens one of
   the other two doors - one which does NOT contain the car - and then
   gives the contestant the chance to switch to the remaining unopened
   door if they wish.  Should the contestant switch?
   
   We know from past shows that this is always how the game works, that 
   the car is equally likely to be behind any of the three doors, and that
   Monty Hall is equally likely to open either door when he has a choice.
   
   NOTE:  The above may or may not correspond to the actual operation of
   the ancient game show "Let's Make a Deal" that Monty Hall hosted.