Earlier quoted context omitted.
Yeah, I think we're agreeing. :) So it turns out, before discovering the bug, I actually wrote code to find the optimal sequence when your choices are restricted to integers. I thought, along the same lines as you, "maybe if you burn 165 or 170 or something in the first non-zero term, then you could burn less on the 14 turn and still land." And this is how I know it's not possible, at least with integer burn rates. :…
I think they are saying that you need to switch to 199.999... lbs/s for all the 200 lbs/s burns, not just the last one. Just trying to clarify where you seem to be speaking past each other, though it seems that this might simply lead to a non-optimal strategy (i.e. taking more time to land than theoretically possible, however minute the difference is).
>switch to 199.999... lbs/s for all the 200 lbs/s burns, not just the last one
That's not it. See here: https://news.ycombinator.com/item?id=40685081