[rookie1ja]

Crossing the Desert - Back to the Logic Puzzles
A military car carrying an important letter must cross a desert. There is no petrol station in the desert, and the car’s fuel tank is just enough to take it half way across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters or rope to tow the cars.
How can the letter be delivered?

Spoiler for Solution:

Car - solution
There are 4 cars needed, including the car with the important letter (which travels to the middle of the desert). Its empty tank must be filled to the top to get to the end of desert. The way between the military base (where the cars and petrol is) and the middle of the desert can be divided into 3 thirds. 3 cars will go in their thirds back and forth and overspilling 1/3 of their tanks. This way the tank of the important car will be filled and the letter will be delivered.

Spoiler for old wording:

A military car carrying an important letter must cross a desert. There is no petrol station on the desert and the car has space only for petrol that lasts to the middle of the desert. There are also other cars (which have the same fuel capacity) that can transfer their petrol to one another.
How can the letter be delivered?

[AyD3n]

4 cars:
1/4 of the way (each car used half their petrol), 2 cars fills the other 2 to full (leaves 2 empty and 2 full)
1/2 of the way, the 2 remaining cars used half of available petrol. 1 car gives the rest of its petrol to the car with the important letter.
car with letter has enough petrol to make the remaining half journey.

[rookie1ja]

Quote

4 cars:
1/4 of the way (each car used half their petrol), 2 cars fills the other 2 to full (leaves 2 empty and 2 full)
1/2 of the way, the 2 remaining cars used half of available petrol. 1 car gives the rest of its petrol to the car with the important letter.
car with letter has enough petrol to make the remaining half journey.

That might fit the conditions as well, since I have not written that all supporting cars have to return to the base.

[esearing]

2 or possibly 3 cars are needed.
The first car can tow the other car in neutral, at which point the 2nd car delivers the letter. 3 if gas milage is affected by the towing.

[Georgew]

Or....we could just do what we do in the military
Email it.

[slasecki]

You only need three cars, but two will be left in the dessert
Two cars leave from the start point. At the quarter point, cars A and B have only 1/2 tank left. Car B, gives all its fuel to car A. Car B is abandoned and Car A has a full tank which now can continue 1/2 way across the dessert. Now it has run out of gas at 3/4 of the way, but car C which has left from the opposite end of the dessert, is there to meet car C. It only has 1/2 tank, but it fills Car A to 1/2 which is enough to travel the remainder of the distance. Car C is also abandoned. Note, only the cars have been abandoned, the people have always joined in car A.

[schmiggen]

Quote

You only need three cars, but two will be left in the dessert
Two cars leave from the start point. At the quarter point, cars A and B have only 1/2 tank left. Car B, gives all its fuel to car A. Car B is abandoned and Car A has a full tank which now can continue 1/2 way across the dessert. Now it has run out of gas at 3/4 of the way, but car C which has left from the opposite end of the dessert, is there to meet car C. It only has 1/2 tank, but it fills Car A to 1/2 which is enough to travel the remainder of the distance. Car C is also abandoned. Note, only the cars have been abandoned, the people have always joined in car A. <!-- s:D --><!-- s:D -->

Unless the military has set up a system for delivering mail via the abandonment of vehicles (seems unlikely) beforehand, there is no way the driver of car C will know to come or to be waiting for car A from the destination side of the desert. And if there were some means to communicate the need for this, that means there would be a way to communicate the contents of the letter. Granted, it is likely to contain top-secret material, and if there were no reliable encrypting system in place for the long-distance communications of the military in the given locations then I guess they could say they were coming and needed help. But of course, if they were afraid someone unfriendly were listening in, they wouldn't want to give away the location, route, and destination of a courier delivering such important information, right?

I think the problem inherently requires that all the cars start from the same location, even though it doesn't say so outright.

[j0k3r]

hi slasecki,
I can't figure out what's your solution.
Let me know is it possible with 3 cars?
Following is your solution?

Car
A = car A
B = car B
C = car C
Gas status
f = full gas
h = half gas
z = zero gas
Place point
0 is start point
1 is quarter point
2 is half point
3 is 3/4 point
4 is goal

Initial.

You only need three cars

A f 0
B f 0
C f 0

Move 1.

Two cars leave from the start point.
At the quarter point, cars A and B have only 1/2 tank left.

A h 1
B h 1
C f 0

Move 2.

Car B, gives all its fuel to car A.
Car A has a full tank

A f 1
B z 1
C f 0

Move 3.

now Car A can continue 1/2 way across the dessert.

A h 2
B z 1
C f 0

Move 4.
is it your next move?

Now it has run out of gas at 3/4 of the way

A z 3
B z 1
C f 0

So, I think car C can't reach to A.

[Slackarius]

If going from the example where there is no communication from the base on the other end of the desert, it is possible still to get the letter across but will require four vehicles.


Base A -----> 25% -----> 50% ------> 75% -----> Base B

All four depart from base A together and travel to the quarter waypoint.
At this point two of the vehicles transfer their remaining fuel to the other two vehicles giving them both a full tank.

The two vehicles, with full tanks, now travel together to the halfway point. One of the cars fills up the other giving it a full tank. Then that vehicle is able to make the remaining distance across the desert with it's full tank.

Now this gets trickier when trying to mount an operation in which the vehicles are not abandoned...I have yet to figure out a solution for that.

[slasecki]

Quote

You only need three cars, but two will be left in the dessert
Two cars leave from the start point. At the quarter point, cars A and B have only 1/2 tank left. Car B, gives all its fuel to car A. Car B is abandoned and Car A has a full tank which now can continue 1/2 way across the dessert. Now it has run out of gas at 3/4 of the way, but car C which has left from the opposite end of the dessert, is there to meet car C. It only has 1/2 tank, but it fills Car A to 1/2 which is enough to travel the remainder of the distance. Car C is also abandoned. Note, only the cars have been abandoned, the people have always joined in car A.

For simplicity, let's assume that the dessert is 100 miles.
I will try to clarify this for you. When Car A and B reach the 25 mile marker, Car B gives all of its fuel to Car A. Now Car A has a full tank and continue an additonal 50 miles. This brings Car A to the 75 mile marker, where it meets with Car C who departed from the end point to help retreive this letter. Since it left with a full tank of gas and has now traveled 25 miles, it now also only has 1/2 tank left which it gives to Car A. Car A can now proceed to the end point.

This problem was stated as merely a problem with fuel, not that we are completing this task at a time when phones are unavailable as well. I don't think it is at all unrealitic to think that the delivery of the letter may be accomplished by both parties working together as a team.