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November 8th, 2019, 02:31 AM   #1
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Math Focus: Calculus
Question How do I find the least number of times a shuttle can go from one place to another?

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 riddle instead of just guessing or trying to play Where's wally with the question.

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 had lesser weights, $52$, $46$ and $49$ kilograms respectively. The latter however does not know how to pilot the rescue shuttle. After thinking a wisely they came up with a solution and found a way to transport the all four to the nearby spaceship. How many times the least possible the rescue shuttle must cross to carry the astronauts?.
The alternatives given in my book are as follows:

$\begin{array}{ll}
1.&9\\
2.&8\\
3.&7\\
4.&4\\
\end{array}$

I don't know really what can sort of thing should I do to solve this riddle. In my attempt to solve I thought that the way to minimize the 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?.

The answer supposedly according to the answers sheet in my book is $7$ but I have no idea how to get there.

Can somebody guide me on exactly which sort of steps or algorithm (if any) can be used to solve this riddle?.
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Last edited by Chemist116; November 8th, 2019 at 02:33 AM. Reason: added information
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November 8th, 2019, 03:05 AM   #2
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1) 46 and 49 to safety
2) 46 back to the station
3) 46 and 52 to safety
4) 46 back to the station
5) 100 to safety
6) 52 back to the station
7) 46 and 52 to safety
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November 8th, 2019, 01:55 PM   #3
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Quote:
The latter however does not know how to pilot the rescue shuttle.
Who is this referring to?
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November 8th, 2019, 04:50 PM   #4
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James, 49 kilograms.
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