[martincmartin]

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 checked all 201^9 combinations, with a few optimizations to cut down the search space.

That's different than what you said, of using floating point for the last burn. But it is in a similar spirit.

[schiffern]

  >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."

That's not exactly what I was thinking.

Clearly that won't work, because just by changing the least significant digit (ie adding 1e-8 lb/s) in step t=70 seconds, you "blow past" the soft landing window, in part due to the bug.

Evidently the move played at t=70 seconds is, in effect, too 'course-grained' to effectively target the (small) soft landing window. By shifting your "subtract 1e-8 lb/s" move (ie playing 199.99999999 lb/s) later and later in the burn, you effectively make it more and more fine-grained (for a minimum fuel penalty) until you can achieve that soft landing.

Thanks again. I'm not sure who's right, but it's certainly a very stimulating problem!

[necovek]

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).

[schiffern]

  >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

[konstantinua00]

speaking of speaking past each other

> and then replace one of the subsequent 200 lbs/second inputs with 199.99999999 lbs/second

> replace one

indeed not the last one, but no, not "all"