Interview question, testing a sorting network
The question is ambiguous, although sometimes interview questions are intentionally ambiguous to prompt a discussion of the ambiguities.

One way to look at it is, if you are verifying a design for a 4-input sorting network, how many input sequences are needed to be sure the implementation is correct. If you don't know anything about how it's implemented, then you need to test all $4!$ permutations of four values to be absolutely certain the implementation is correct.

Another way to look at it is, if you manufacture the circuit, how many input sequences do you need to apply to each device during testing to be sure the circuit was manufactured correctly. In this case you would usually take the design as a given, so you don't need to cover all $4!$ permutations, you just need enough inputs to cover the interesting cases for each element of the circuit. I'm guessing this was the intention of the question, and I'm guessing that only two cases are considered interesting for each MinMax2 component (A&gt;B and A&lt;B). There's also the A=B case, but you can argue the behavior of the MinMax2 is a don't-care when A=B. 

This isn't realistic, since in practice you would need more than two cases to make sure all of the transistors and wires inside the MinMax2 component were manufactured correctly. But I'll assume that we're just trying to cover two cases for each MinMax2.

In that case, if the inputs are A through D where A &lt; B &lt; C &lt; D, then only two inputs are necessary to cover both cases for each MinMax2: A, C, B, D and D, C, B, A. The first covers the "no-swap" case for each MinMax2, and the second covers the "swap" case for each MinMax2.