Mars Lander Fuel puzzle discussion

Feel free to send your feedback or ask some help here!

Level 2 - Fuel Optimization

hy i am not able to control hs speed … any idea ?

You can adjust the angle, to control hs speed.

Hello. Mars landers, this can help you :

Much as you can watch a replay of other player’s multiplayer games by browsing the leaderboards, I think being able to watch a replay of the results of other players’ optimization submissions would be very educational. Wouldn’t it be nice to see how the #1 coder landed the Mars Lander with so little fuel expenditure? Of course this is hampered a bit by the fact that the actual scored verifications aren’t even visible to the submitter. Is this something we could see in the future please?


I agree. Or simply the maximum remaining fuel achieved in individual test cases (not just the the sum for all test cases) is useful too.

Achieved figures for reference:
Test case 2.1: 341L
Test case 2.2: 372L
Test case 2.3: 517L
Test case 2.4: 545L
Test case 2.5: 728L
Total: 2503L



Did anyone ever try to figure out theoretical maximum limits for each tracks ?

I mean the first obvious limit is the starting fuel.

But then taking into account starting position plus other parameters and constraints, there should be some mathematical formula to devise a fuel limit.

I’m not from a math background but I made some calculation of this kind for the first track removing the X component that gave me a limit of 364 (by removing X component i mean moving the ship right over the landing ground in the problem, allowing a straight landing).

But I just can’t figure how I could integrate the X component into the calculation.

For X movements implies angle rotation which impact Y so it’s more complicated.

Anyone got a an idea :wink: ?


Hey !

I just achieved the first 3 test cases using a not so intelligent algorithm :smile:

Now I’m facing the two last test cases and clearly my tinkering will not be enough. I have to get out of my confort zone and learn new things, which is why I’m here, but I really don’t know where to start.

If someone has some guidelines or a link with some theory I could use it’ll be appreciated. Not looking for a solution but something to understand and then use in my code. (It can be in French or English).

Achieved figures for reference:
Test case 2.1: 338L
Test case 2.2: 367L
Test case 2.3: 510L
Test case 2.4: 539L
Test case 2.5: 722L
Total: 2475L

While simulating speed over time I get discrepencies (minor but still annoying) with what’s shown in the output. I’m only doing simple trigonometry to compute forces so I wonder if there are approximations to be known (like float rounding) in the engine?


Same question

I’m using floats for the shuttle position and speed parameters and all simulation calculations. As far as I remember, if I wanted the exact (integer) results for the shuttle parameters I round to nearest, after all commands for the turns are applied:

(float turn0X, float turn0y) -> apply turn0 rotate and power using float calculations ->
(float turn1X, float turn1y) -> apply turn1 rotate and power using float calculations ->
(float turn2X, float turn2y) -> apply turn2 rotate and power using float calculations ->
(float turn3X, float turn3y)

print(round(turn3X)) // To see if the X for turn 3 matches the X for turn 3 from the CG platform
print(round(turn3Y)) // To see if the Y for turn 3 matches the Y for turn 3 from the CG platform

I am trying to display the landers’ landing path with Python turtle. But the drawing is really slow. This is a population of 200. I am afraid it could not finish in a given amount of time. Is this due to the python turtle package or my algoritem ? Or this is correct?

How can i reduce his vertical speed

I had the same problem and finally solved it.
Remember that given a constant acceleration,

speed(t) = initial_speed + acceleration * t
position(t) = initial_position + initial_speed * t + 1/2 * acceleration * t^2

Here is my simulation sequence

update rotate and power
calculate acceleration vector (combining power/orientation and gravity)
position += speed + 1/2 * acceleration
speed += acceleration

acceleration, speed and position are float 2D vectors.
I never round values.

With that I managed to exactly reproduce every position and speed.

Hope it will help you


It’s been a long time since I messed with this but my memory is that the sim is keeping your position in a float (maybe a double), but it gives you the rounded number in the inputs. Or at least, I built my bot with that assumption and didn’t have any mismatches between expected and actual position.


for anyone looking to simulate the next turn, this was pretty accurate for me

    const radians = R * (Math.PI / 180)
    const xAcc = Math.sin(radians) * P
    const yAcc = Math.cos(radians) * P - gravity
    HS -= xAcc
    VS += yAcc
    const newX = X + HS - xAcc * 0.5
    const newY = Y + VS + yAcc * 0.5 + gravity


I am trying to solve by solving this system of equation.
I’m stuck because I can’t isolate more than one unknown.
Do you think is possible?

I am not very smart and dont understand this simulation, it was not working for me so I rewrited like so:

//Be aware of gravity sign
//Convert degree to radians for sin() / cos() methods
radians = Math.toRadians(rotateAngle);
//sin() of 90 / -90 will return 1 / -1 so if shuttle pointing left/right full power goes along X axis
xAcc = Math.sin(radians) * power;
//cos() of 0 / 180 = 1 / -1
yAcc = Math.cos(radians) * power - MARS_GRAVITY;
//We need to reverse X acceleration sign because in puzzle positive acceleration is along x axis, but in
//the formula positive sin(90) = 1 is left (conter-clockwise)
x += hSpeed - xAcc * 0.5;
y += vSpeed + yAcc * 0.5;
//If simple - we applying “turn” acceleration as half of it because acceleration is not instant, but after the
//turn we save full acceleration to speed value as we reach it during turn
hSpeed -= xAcc;
vSpeed += yAcc;

Hi all.
I’m trying to learn Genetic algo and apply it to this mars lander game.
Just to be sure I got it right

For each input :
   update ship status
     generate a list of random (angle, power) tuple (that's the population in GA)
        apply each tuple to the ship to get a new ship status and evaluate a score ,
        sort the result by score , to get the best 30% plus 20% random
        complete this new list with  mix of them (the crossover in GA tutorial)
        repeat the above 3 steps until you get a short list of result:
 print the best gene (tuple)

Is my above statement correct ??
If so, based on the previous post i understand how apply to the ship.
But how to evaluate the best score since the goal change over time ??
first goal use less fuel and later then land slow and straight ??

or did i get this completely wrong ??