Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. — Sherlock Holmes

In science, observations are made and a number of hypotheses are constructed to explain these observations. Competing hypotheses are analyzed and discarded by the method of elimination which Sherlock Holmes uses. The one hypothesis that survives is then taken to be truth. Of course, there's the need for positive evidence to prove a hypothesis true but, by far, competing hypotheses are dealt with by elimination.

So, we could say that the hypothesis that we agree is one we arrived at NOT by confirmation only but also by disconfirming other hypotheses. My question concerns one aspect of such a method - that this does NOT imply that you understood anything at all.

To illustrate:

Imagine a multiple choice question like below:

What is 8 + 16?
a) apple
b) 24

Even if you do NOT understand math you can arrive, like in science, at the "correct" answer by the method of elimination like so: a) isn't the correct answer because it's not a number. So the answer must be b).

Notice that we arrived at the "correct" answer without any understanding of mathematics simply by using Sherlock's method.

Is a similar thing happening in science? Could it be that we don't actually understand anything at all?

One issue with what I'm saying is that we not only disconfirm but also confirm hypotheses. It's not that we rely ONLY on the method of elimination. However, if Karl Popper is correct then we can never ever confirm a scientific hypothesis. We can only eliminate possibilities which brings us back to my question:

Do we understand anything in science?