A very interesting problem. I could not find a solution with 3 cars. Have you ever seen a proof or any argument why 4 are necessary?
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
No I haven't.
But I have been thinking how to rescue the empty cars.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Only one question. It doesn't says that you will be able to tow another car! Even if you can. It will use more patrol that's wouldn't take you to quarter a desert per car!
Creeper_mode - Amateur Math solver
Love Logic Puzzles.
[hide = 4 Cars without salvage]My solution also uses 4 cars, but each car should be able to return to the start point (3 cars) or get to the other side (1 car)
Each car has a different role and travels different distances
Car 1: Travel 1/6, Transfer 1/6 to either Car 2 or Car 3, Return 1/6
Car 2: Travel 1/6, Receive 1/6 from Car 1, Travel another 1/6, Transfer 1/6, Return 1/6, Receive 1/6 from Car 1, Return 1/6
Car 3: Travel 1/6, Receive 1/6 from Car 1, Travel another 1/6, Receive 1/6 from Car 2, Travel 1/6, Transfer 1/6 to Car 4, Return 1/6, Receive 1/6 from Car 2, Travel 1/6, Receive 1/6 from Car 1, Travel 1/6
Car 4 [With VIP]: Travel 1/6, Receive 1/6 from Car 1, Travel another 1/6, Receive 1/6 from Car 2, Travel 1/6, Receive 1/6 to Car 4, Travel 1/2 to destination
The obvious issue is the time waiting for Cars 1 and 2 to constantly return and refill. But it is feasible.[/hide]