"The problem with this question is that you could just randomly pick 10 and find the right answer without having to do any calculation. Meh."
True, but consider it as a test of intuition. Why pick 10? Because it is √100 (or maybe because it is log(100)). The intuitive approach doesn't get you the perfect answer, but it gets you into the ballpark.
Having picked 10, we might then realise that the 'worst case' changes and gets worse the higher up the building we go, so then intuition might say that we need to tweak the step size somehow to get down the size of the worst case. Or we might think that that step size works fine for a 100 storey building, but what about a 10,000 storey building? Our intuition is telling us the algorithm can still be refined.
But then maybe we look at what you wrote and think to ourselves, 'what if the best sequence isn't linear, but is based off the fibonacci sequence instead?'. And then maybe we tootle around a bit with our theoretical fibonacci based algorithm. Maybe we decide it isn't quite as good because it has a worse worse case. But then we might have another intuition, that perhaps there are other ways of measuring which is the better algorithm. So lets say we measure the average, and lo and behold the theoretical fibonacci algorithm has a better average, but a worse worst case. We might be confused at that point as to which one was 'better', because they are each better by different measures. But now we can put it into a broader context and reason about which one to use in which situation.
Moreover recognising that this sort of problem can be decomposed into smaller chunks is not a bad thing. Having a good intuition towards decomposition is an important part of design.
True, but consider it as a test of intuition. Why pick 10? Because it is √100 (or maybe because it is log(100)). The intuitive approach doesn't get you the perfect answer, but it gets you into the ballpark.
Having picked 10, we might then realise that the 'worst case' changes and gets worse the higher up the building we go, so then intuition might say that we need to tweak the step size somehow to get down the size of the worst case. Or we might think that that step size works fine for a 100 storey building, but what about a 10,000 storey building? Our intuition is telling us the algorithm can still be refined.
But then maybe we look at what you wrote and think to ourselves, 'what if the best sequence isn't linear, but is based off the fibonacci sequence instead?'. And then maybe we tootle around a bit with our theoretical fibonacci based algorithm. Maybe we decide it isn't quite as good because it has a worse worse case. But then we might have another intuition, that perhaps there are other ways of measuring which is the better algorithm. So lets say we measure the average, and lo and behold the theoretical fibonacci algorithm has a better average, but a worse worst case. We might be confused at that point as to which one was 'better', because they are each better by different measures. But now we can put it into a broader context and reason about which one to use in which situation.
Moreover recognising that this sort of problem can be decomposed into smaller chunks is not a bad thing. Having a good intuition towards decomposition is an important part of design.