I have found that my ability to solve complex problems is to some extent separate from my willpower to solve those problems.

One way I've measured my ability has been by solving Sudoku puzzles on my mobile phone. I try to solve them without "pencilmarks", so that I put down a number only when I'm sure where it belongs, in an attempt to hone my working memory and focus.

I've found that, when my brain is not working that well, I keep finding that I've just retraced the same logical steps from just a few moments ago, because I've forgotten the conclusion in the meanwhile.

I've also found that, when I feel exhausted and not at all like doing any work, my Sudoku solving skills are actually quite good - so feeling tired can be separate from actual (in)ability.