Gas truck in the desert

Reasoning ...
OK. Each point in the straight line journey must be traversed an odd number of times. Thus if you could carry enough gas to get across, you would traverse each point only once.

Logically then, to minimize the total distance driven you want to maximize those points traversed only once, since this is the most efficient. Once this is done, you want to maximize those points that are traversed 3 times; then maximize those points traversed 5 times, etc.

Now, if you can get to the middle and have a full tank, you can get across, and you've maximized the distance traversed only once.

So how do you get to the middle and have a full tank? Well, if you can reach a point A, which is 1/6 (= 1/2 * 1/3) of the way before the middle (1/2 - 1/6 = 1/3 of the way across) and if you can have 2 loads of gas there, then you can get to the middle with 1 tank. Like this:

Travel from point A to middle, use 1/3 tank of gas
Deposit 1/3 yank in the middle
Use remaining 1/3 tank to get back to Point A.
Travel from point A to middle, use 1/3 tank of gas
You have 2/3 tank, added to the 1/3 you left beofre is 2 tanks.

OK so far?

SO how do you get to point A with 2 tanks? Well if you can reach point B which is 1/10 (= 1/2 * 1/5) of the way before point A (1/3 - 1/10 = 7/30 of the way across) with 3 tanks, then you can get to point A with 2 tanks. Like this.

Travel from point B to point A, use 1/5 tank;
Deposit 3/5 tank at point A;
Return to point B using the remaining 1/5 tank;
Travel from point B to point A a second time, use 1/5 tank;
Deposit 3/5 tank at point A;
Return to point B using the remaining 1/5 tank;
Travel from point B to point A a third time, use 1/5 tank;
You arrive at point A with 4/5 tank, in addition to the 6/5 tank (2 * 3/5) that you've previously deposited, making 2 full tanks at point A.

So how do you get to point B with 3 tanks? Well, if you can reach point C which is 1/14 (= 1/2 * 1/7) of the way before point B (7/30 - 1/14 = 17/105 of the way across) with 4 tanks, then you can get to point B with 3 tanks. Like this:

Travel from C to B, use 1/7 tank;
Deposit 5/7 tank at B;
Return to C using the remaining 1/7 tank.
Travel from C to B a second time, use 1/7 tank;
Deposit 5/7 tank at B; (total left = 2 * 5/7 = 10/7);
Return to C using the remaining 1/7 tank.
Travel from C to B a third time, use 1/7 tank;
Deposit 5/7 tank at B; (total left = 3 * 5/7 = 15/7)
Return to C using the remaining 1/7 tank.
Travel from C to B a fourth time, use 1/7 tank;
You have 6/7 tank, added to the 15/7 tank is 21/7 or 3 full tanks.

So how do you get to point C with 4 tanks? Well, if you can reach point D which is 1/18 (= 1/2 * 1/9) of the way before point C (17/105 - 1/18 = 67/642 of the way across) with 5 tanks, then you can get to point C with 4 tanks. Like this:

Etc etc etc ....

Thid looks like an infinite series, but you can cut it after a couple of more iterations. The answer is about 7 + tankfulls.

Did that help? (I hope I didn't make any arithmetic errors in this .. basically the method is correct).

Works for me. You can actually go 1.01+ times the length of the desert with 8 loads.

My old mate, and a friend of Crocodile Dundee asks;
"I'm intrigued. Who is this Nobody, and did they answer correctly?"

That would be me, myself and I. Yes, in 1.5 trips.


"Try reading the question again."

Thank you, I just managed that and again scored a point. I had no problem with the question. It was the answer that eluded me.

"This is the Spaceship journey to planet X riddle. Not the Bananas in the desert by camel riddle."

Again my thanks for clearing up the confusion due to the order of the words. I thought it was the old camel in the Spaceship riddle.


"You've been doing too many pure math riddles Try."

They appear to be the only ones that don't excite your interest.

"After a while it starts to affect your basic english comprehension skills."

Capital ?'E' in English if you please. I am not that effected.


"Verily I suggest a reduction in thou intake of mead good knight."

Good advice Doc, and good night to you too.


However, it would be remiss of me, if the rumours circulating the corridors of AtoNo are to be believed that you are hiding your talents under a coolabah tree by not mentioning your trophy in the Lucindale Shears competition (now in its 13th year). After all this is the largest sheep shearing competition in South Australia, and in the top 10 Australia wide.

If true, many congratulations. :wink:

Pjnbarb, I remember seeing an answer similar to yours somewhere. I would say you've got the optimal solution. Well done.

Try, I'm in training as we speak old mate. This year I'm goin' for gold.
If I'm successful I promise to retire and take up a career in pure math riddles, OK?

"This year I'm goin' for gold."

Adrian, fair dinkum mate we should all have goals.

"If I'm successful I promise to retire…"

I am betting on you, but personnel reckon you retired long ago. :wink: