You're a cube living in reality n. Your goal is to get to the exit door, the purple one. But you can't go straight there. You'll need to use your n-k (k > 1) past realities to get to the objective.
The yellow door is your magical portal to your last reality. Once you get there use SPACE to move and fix the avaliable platforms where you need in the present reality. Then suicide :(
It's all about what you do in the present depending on what you could have done in the past... Once you lived your present, you'll only be able to watch it one time.