Suppose that we have on the moon a space station which is the only source of fuel and on it there are unlimited number of identical spaceships, We want to send one of them to Mars, each spaceship has a fuel capacity to allow it to fly exactly 1/4 way to Mars (without fuel the spaceship will miss its direction and may explode!).
Each spaceship has the ability to refuel by a second spaceship through a specific connection between them without loss of speed . What is the fewest number of spaceships necessary to accomplish this mission without losing any one of them?
Note:1- Each spaceship must have enough fuel to return safe to the base space station .
2- The time and fuel consumption of refueling can be ignored. (so we can also assume that one spaceship can refuel more than one spaceship at the same time).