Distinct Karnaugh Maps grouping?

Question

I got a table truth with some minterns which I mapped to a Karnaugh Map, then I can see an obvious choice for grouping. But I'm wondering wether in this case is possible to do any other different to the first one?

Answer 1

We can prove this is minimal as follows.

Consider the entry 001. The maximal grouping that contains 001 is the blue domino. Likewise, the maximal grouping that contains 110 is the red domino. So every covering must contain subgroupings of these two dominos, and the two dominos cover the set of $1$s. So this is optimal.

Of course, there are other coverings. For instance, you can add a redundant domino over the middle $1$s. You can also bubble individual cells, which is a trivial covering that gets you nowhere.