Author |
Topic: A trip around the world less than 80 days (Read 766 times) |
|
Christine
Full Member
Posts: 159
|
 |
A trip around the world less than 80 days
« on: Jun 27th, 2008, 10:13pm » |
 Quote  Modify
|
There is only one airport on a fictional planet, and that is on the north pole. There are 3 airplanes and lots of fuel at the airport. A full tank of an airplane lasts exactly to the south pole, however the airplanes can transfer their fuel to one another.
Your mission is to fly round the globe with at least one airplane, making sure to cross the south pole. All airplanes must return to the airport.
|
|
 IP Logged |
|
|
|
rmsgrey
Uberpuzzler
    
Gender: 
Posts: 2873
|
|
Re: A trip around the world less than 80 days
« Reply #1 on: Jun 28th, 2008, 10:42am » |
Quote Modify
|
| hidden: |
All three planes launch and fly together for 1/4 tank, then plane C transfers 1/4 tank to each of the others, leaving it just enough fuel to return to the airport.
After burning another 1/4 tank each, plane B transfers 1/4 to plane A over the equator, leaving it just enough fuel to return to the airport.
As plane B lands, plane C launches with a full tank, flying in the opposite direction - at the same time, plane A is down to 1/2 a tank and is directly over the south pole.
Plane C meets plane A at the equator just as plane A runs out of fuel, and transfers 1/4 tank. At the same time, a refueled plane B launches to meet them.
Plane B meets the other two planes as their tanks empty, and shares its 3/4 tank with them, giving all three just enough fuel to make it home.
|
|
|
IP Logged |
|
|
|
Benny
Uberpuzzler
Gender:
Posts: 1024
|
|
Re: A trip around the world less than 80 days
« Reply #2 on: Jun 28th, 2008, 10:52am » |
Quote Modify
|
rmsgrey, you beat me to it. I was going to post today.
The question i had on my mind was:
so where else would the planes land if there is only one airport?
I assume that we can still work out the problem.
|
|
IP Logged |
If we want to understand our world or how to change it we must first understand the rational choices that shape it.
|
|
|
Benny
Uberpuzzler
Gender:
Posts: 1024
|
|
Re: A trip around the world less than 80 days
« Reply #3 on: Jun 28th, 2008, 12:02pm » |
Quote Modify
|
How about
Plane 1, 2 and 3 start flying with tanks full.
Just when 1/4th of the distance to the south pole has been reached, plane 3 transfers 1/4th of the fuel capacity to plane 2, and 1/4th of fuel capacity to plane 1.
This means that plane 3 now has 1-(3*1/4) = 1/4 of total fuel capacity. With it, the plane immediately goes back to the north pole, barely making the trip and refuels.
When plane 1 and 2 reaches halfway to the South pole, plane 2 transfers 1/4 of total fuel capacity to plane 1. Plane 1 has a full tank, plane 2 has initial - trip loss + gain from plane 3 - loss to plane 1 = 1-1/2+1/4-1/4 = 1/2 of total fuel capacity. It starts return journey immediately.
Upon return of the second plane, both plane 2 and 3 start journey immediately with filled tanks.
When they are 1/4th to the south, in the "other way round", plane 3 gives 1/4th of the total tank capacity to plane 2 and returns immediately to base. Upon arrival it refills and starts again to meet plane 1. (**)
With a full tank plane 2 goes 1/4th of the distance to south pole, and refills plane 1 which has an empty tank. Now plane 2 has 1/2 tank full and plane 1 has 1/4 tank full. Plane 2 starts return immediately.
When plane 1 will have an empty tank, it will meet plane 3 again [see line (**)] and then another refill, and all are home.
Assumption: refill takes zero time.
|
|
IP Logged |
If we want to understand our world or how to change it we must first understand the rational choices that shape it.
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: A trip around the world less than 80 days
« Reply #4 on: Jun 28th, 2008, 2:05pm » |
Quote Modify
|
It also works.
But I prefer rmsgrey's. It is more symmetrical and uses a bit less fuel.
|
|
IP Logged |
|
|
|
rmsgrey
Uberpuzzler
Gender:
Posts: 2873
|
|
Re: A trip around the world less than 80 days
« Reply #5 on: Jun 29th, 2008, 6:23am » |
Quote Modify
|
on Jun 28th, 2008, 2:05pm, Grimbal wrote:It also works.
But I prefer rmsgrey's. It is more symmetrical and uses a bit less fuel.
|
|
And it doesn't require instantaneous refueling on the ground 
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print