Moon Landing

[hibiki]

I was playing with the game Moon Landing for HP25 published here:

http://www.hpmuseum.org/software/25moonld.htm

I adapted it to HP34C, as I do not have the 25. And also for HP32SII.

It started at 500 feet height, -50 feet/s speed and 120 units of fuel. So my best sequence of burns that solve the problem is 0-0-0-0-0-5-5-80 remaining 30 units of fuel and only 8 seconds (steps) with 3 fuel burns. This is my best and faster landing sequence. There are also other solution sequences , with less amounts of fuel remaining and more landing time.

Solving for the equations used, i found the constant amount of fuel consumption to land the spaceship. It is 7.5 units per burn, doing 20 burns. This of course is 30 units more than the available amount of fuel. So this answer does not solve the problem.

So, now I was looking at the HP67 game version. It starts only with 60 units of fuel, and the same height and speed of the HP25 version. Much less fuel than my best solution for the HP25. Is it possilble to solve with this HP67 version ? Is there any algorithm to minimize the fuel consumption besides landing safely the spaceship ?