Introduction to Logic


There is a combination safe with four switches on the front, each with three positions (low, medium, and high). If the switches are set into an opening combination, then when you try to open the safe, it will open; otherwise, no dice. In general, there are 3^4 = 81 possible combinations. However, this is a cheap safe; and only two of the switches actually matter; if you set those two switches right, the safe will open. Unfortunately, you do not know which are the important switches or which positions work. What is the minimum number of combinations you must try that will *guarantee* to open the safe? What is your plan?