How are you going to judge someone's submission to your challenge?
It is easy. The following will be checked:
A. Does the submission include calculations using basic astrophysical principles of space navigation and travel the amount of fuel (kg) (or energy (J)) required to complete a manned Moon return trip and a manned planet Mars return trip from being ejected into space from orbit around Earth towards the Moon and planet Mars by external combustion chambers (also known as rockets), i.e. are two different trips described (one to the Moon, one to planet Mars),
B. Does the submission include a description of the spacecraft incl. its masses before/after the various manoeuvers of the trips, any heat shield(s), if fitted, the engines and fuel tanks that can carry the amount of fuel using 1960 or 2016 technology, the accommodation and gear for the persons aboard and
C. Does the submission show that it is actually feasible to do the trips.
A submission shall also include, i.a.:-
1. Mass (kg)/speed (m/s)/altitude (m) of spacecraft/fuel in orbit of Earth (ready to go) and how it got there!
2. Mass (kg)/speed (m/s)/direction of spacecraft/fuel after departure orbit Earth heading for location X in space and on to Moon and Mars + calculations (location X is where Moon/Mars gravity equals Earth gravity in space).
3. Mass (kg)/speed (m/s)/direction of spacecraft/fuel prior arrival Moon/Mars + calculations.
4. Mass (kg)/speed (m/s)/altitude (m) of spacecraft/fuel in orbit around Moon/Mars - if applicable.
5. Mass (kg)/speed (m/s) of spacecraft/fuel in orbit Moon/Mars and prior landing - if applicable.
6. Mass (kg) of spacecraft/fuel after landing Moon/Mars.
7. Mass (kg) of spacecraft/fuel prior departure Moon/Mars.
8. Mass (kg)/speed (m/s)/altitude (m) of spacecraft/fuel in orbit Moon/Mars prior departure to return Earth - if applicable.
9. Mass (kg)/speed (m/s)/direction of spacecraft/fuel after departure orbit Moon/Mars heading for location X in space and on to Earth + calculations.
10. Trajectories - locations in space at regular intervals to confirm that you are heading in the right direction
11. Mass (kg)/speed (m/s)/direction of spacecraft just prior re-entry Earth.
12. Trajectory of re-entry, incl. start location (position/altitude), directions in 3D, altitudes, velocities in 3D every minute from start to end (parachutes deployed).
13. Landing (details).
Manoeuvres to leave/enter orbits and to land/depart must be explained in detail incl. locations/times, etc.
If all above information is provided, individual items will be checked for correctness.
As the spacecraft travels between planets orbiting the Sun, the gravity of the latter must evidently be considered, i.e. during the trip the Sun will always attract the spacecraft.