Tower of Hanoi Rules - A possible New Problem

I have been meaning to submit this problem for quite some time now. I hope that it is pitched at the right level to encourage people to solve it. The Tower of Hanoi is a really elegant problem so this should be a fun problem to solve. Rodion, the problem description and setter should now be in your e-mail account.

Rodion, many thanks for your latest problem. It is one of the best yet. I have enjoyed experimenting with the behaviour of the system, despite the fact that I made a complete pig's ear of my initial attempts to solve it. I wrote a Python program to solve the first problem. This generated a flight plan to paste into the answer box. I then modified this program to solve the second of the two problems. I couldn't understand why it no longer worked, until I realised that the flight was often stopping before the expected end point. After careful comparison with your simulation I discovered that there was a bug in my code. I had recorded the mass of the empty rocket as 1000 kg rather than 10000kg so the simulation was simply running out of fuel. Because of the generous tolerance on the first problem this error hadn't caused any issues, otherwise I would have spotted it much sooner. After correcting this problem everything seemed fine. Achieving the tighter tolerance was relatively easy but I soon realised that it was now quite difficult to reach some of the required height and velocity combinations. I have had to put the problem to one side for the moment in order to concentrate on other things. However, I have several ideas that I want to try out and am looking forward to getting back to it when I get a suitable block of free time. I have to take my hat off to Mathias who clearly solved the problem very quickly.