Safecracking

There is a combination safe with four switches on the front, each with three positions – low, medium, and high. 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. You do not know which are the important switches or which positions work. What is the minimum number of combinations you must try to guarantee that you will open the safe?

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