If you take the story literally, yes. If you assume that the problem is slightly more complicated and the author simplified for the benefit of having a readable story, your little notes app does squat.
If the solution for a complicated problem comes to you this way, you have managed to see dozens of moving parts at just the right time, from just the right angle, in your mind. It is incredibly hard to hold on to that, and writing it out in notes takes several pages.
When that solution comes to you, you cling on to it for dear life until you can put it into a form that works - several pages of notes, a test proving your point, a large diagram. Whatever it is. None of those answers can be captured with a phone app.