I introduced this problem into the IT department at my workplace a few years ago and was stunned at the reaction it produced. I thought that I was going to be the victim of physical violence more than once. Even hardware types went off and wrote programs to convince themselves of the solution. I published (in the IT department) several ways of looking at the problem. I think the most direct approach is as follows:
Choose a door and you will be wrong two thirds of the time. Once a door is eliminated (by being opened by Hall) you are still wrong two thirds of the time. So by switching to the remaining door you will be right two thirds of the time.
posted by Barry Allebone
August 27, 2008