I often see this situation in exams and I'd like to know if there is any kind of algorithm or shortcut that I can use to solve this puzzle instead of just guessing.
The problem is as follows:
A space station must be evacuated to a nearby spacecraft which offered help. Four astronauts are trapped in the space station with only one rescue shuttle available to carry them to the other spaceship. However the shuttle has two major limitations; the first is that it has to be piloted manually and the second is that it has a maximum capacity of 100 kilograms, which is exactly the weight of Terry, the first astronaut. The other three, Henry, Charles and James have lesser weights, 52, 46 and 49 kilograms respectively. James, however, does not know how to pilot the rescue shuttle. After thinking, they came up with a solution and found a way to transport all the four to the nearby spaceship. What is the least number of times the rescue shuttle must cross, to carry the astronauts?.
The alternatives given in my book are as follows:
I don't know how to approach this puzzle. I thought that minimizing voyages would meant giving priority to the heaviest passenger first. But I'm confused about the condition which states that the rescue shuttle has to be piloted manually. Does it imply that to go back and fourth must always include a pilot on its way back to pick up the following passenger?
According to the answer sheet, the answer is 7, but I have no idea how to get there.
What sort of steps or algorithm (if any) can be used to solve this puzzle?
I found this in a collection textbook which doesn't indicate the author. I often see this situation in repeated scenarios including, ferries, elevators and so on.