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Tue 3 Feb, 2004 05:42 pm
A rocketship is to go from Earth to Planet X. It is a five day trip, but the rocket only holds enough fuel for 3 days flight. Fuel stations 1, 2 and 3 are 1, 2 and 3 days flight from Earth. The fuel stations are empty, but Earth has an unlimited supply of fuel. The rocketship can leave fuel at stations 1, 2 and 3. What is the minimum number of days required to reach Planet X from Earth, using this rocketship as the mode of transportation?
21 is what I get after a quick look.
My reasoning is that it takes 2 days to get 1 fuel day (FD) to station 1.
You need 2 FDs at station 1 to get 1 FD to station 2.
So that's 4 days just to prepare for station 2. Getting a FD to station 2 takes 4 days (note all the days are including a round trip till the last one).
So basically it takes 8 days to get a FD to station 2.
You need 2 FD at station 2 to get to the destination.
So that's 16 days plus the 5 day last trip to the end for a total of 21 days.
There might be quicker ways, I don't plan to mull them over but maybe trying to leave a FD at the third station will allow for some other tricks.
3 return trips to get 3 FD's to 1 = 6 days
1 return trip to get 1 FD to 2 = 4 days
That leaves 1 FD at 1 and 1 FD at 2. That's all you need to do 1 trip.
So 15 days total.
I still wonder of it could be done in even less. I really don't wanna get sucked into this one though....
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