Urgent Letter
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?
How can the letter be delivered?
Labels: logic, mathemagic
posted by Rajesh Lal at
5:07 PM
24 Comments:
Airmail
Ok, if the letter can't go by air, then the military would arrange for someone to air drop fuel at planned locations.
You need 3 cars with full tanks A,B,C
A with the letter
-when you reach the 1/4 distance point all cars have 3/4 tanks, car C transfer 1/4 tank to A, and a 1/4 tank to B, leaving it with 1/4 tank to return home. Now A +B are full again
-when the reach the 1/2 distance point cars A+B now have 3/4 tanks
-B transfers 1/4 tank to A, leaving it with 1/2 tank for the return trip and car A with a full tank able to reach its final destination
Cam
I'm going to read between the lines and make the following assumptions... please tell me if I am wrong.
1. I have as many cars as I want at the start point, all with the same fuel consumption rate, and a tank big enough to traverse half the desert.
2. At the starting point, there is a fuel station with essentially infinite fuel. However, this fuel cannot be carried by any means except by in the car's gas tank, where it will obviously be used as the car moves.
3. I have other people with me that are able to drive the other cars.
So assuming this is the case...
I take two cars and take them 1/4 of the way.
I take two more to where the other two cars are, and combine the fuel so that I have two cars with full tanks and two cars with empty tanks.
I drive the two cars from the 1/4 point to the halfway point, then combine their fuel so that I have 1 car with a full tank.
Drive this car to the end.
Cam,
You kind of sniped me with the same answer there :P
But... when the cars reach the 1/4 point the have 1/2 a tank left, not 3/4
but can it be done with just 3 cars??
Well, it doesn't say how many cars, so I assume you have as many as you want.. 8 cars will get it across for sure..
8 cars go 25% of the way, half of them transfer all their gas to the other half. Make sure the letter is with one of the 4 cars with gas.
4 cars goto to the 50% mark. again half of them transfer all their gas to the other half. Still keeping the letter with a car that has gas.
2 cars can now make it to the 75% mark. 1 of the cars transfer it's gas to the other car. Don't forget the letter!
1 car with the letter makes it across.
--------------------
6 cars will work too..
6 to 1/3 of the way (they have 1/3 tank each left)
4 cars fill up the remaining 2 cars
2 cars get to 2/3 of the way (they each have 1/3 left)
1 cars transfers it's gas to the other.
Last car gets to the finish just as it runs dry.
Hopefully they were smart enough to keep the letter all the way to the end.
Dang.. i just say Cry Wolf's solution.. well done.. I missed the fact that at the halfway point the car is full and doesn't have to stop at the 75%.
so as Cry Wolf suggested:
4 cars to 25% (fill up 2 from the other 2)
2 cars to 50% (fill up 1 from the other)
1 car to 100%
The title is "urgent letter". Worry about rescuing temporary cars later. I assume that there are plenty of drivers. If not, I'll have to think again.
You start with 4 jeeps A,B,C and D. A has the letter. Go 1/4 of the way. Transfer the fuel from C and D to A and B, so they are full. Now drive another 1/4 of the distance to the half-way position. Transfer the fuel from B to A, so A is full. A can just complete the journey.
OOps. I see that Cry Wolf has already done it that way.
.. as has EB. His post didn't appear until after my "Oops" post.
I used bad math the first time, (didn’t have to abandon cars=too good to be true) so to redeem myself….
Working backwards from the desired objective….
Car at 0.5*D with full tank
-can be achieved with 2 cars with half tanks at this point (0.5+0.5)=1
-we can achieve this by having two cars with full tanks 0.25*D away (will consume half a tank each to cross 0.25*D)
-we can achieve this by having two cars for each of these cars 0.25*D away from these cars (starting point)
(Total 4 cars)
We can, via this method extend D by 0.25*D by doubling the number of cars i.e. given enough cars any distance can be covered
To achieve the distance using 3 cars…..
-3 cars A,B,C go to 1/8*D mark… tanks = A=0.75, B=0.75, C=0.75
-C tops up A+B, tanks= A=1,B=1,C=0.25
-C returns home, fills up again, and meets cars back at 1/8*D mark, tanks = A=1,B=1, C=0.75
-cars continue to 0.25*D mark, tanks= A=0.75, B=0.75, C=0.5
-C tops up A+B tanks, A=1, B=1,C=0
-A+B drive to 0.5*D point tanks = A=0.5, B=0.5
-B tops up A and A with a full tank drives the letter to final destination…..
Hopefully no bad math this time…
Cam
Gee, if they have access to the internet and time enough to send us their problems, can't they just use email? This is a good example of the military-industrial complex looking for elaborate ways of consuming fuel. :)
(Sorry, couldn't resist)
4 cars drive to 1/8 of the way
I haven't seen a military solution.
Here's mine...
Call the cars A, B, C and D
Car A will go all the way.
All cars drive to 1/8 of the way.
Car B gives 1/5 of a tank to Car A......Car A = 87%
Car C gives 1/3 of a tank to Car B......Car B = 80%
Car D gives 2/3 of a tank to Car C......Car C= 67%
Car D is finished.......................Car D = 0%
Cars drive to 1/4 of the way............Car A = 100%
Car B gives 3/10 to Car A...............Car B = 100%
Car C gives 2/3 to Car B................Car C= 17%
Car C is finished
Cars drive to 1/2 of the way
Car B gives 1/2 to Car A ..............Car A = 100%
Car B finished
Car A goes to finish
The fractions were fractions of a full tank, not a fraction of what they had.
At the end, 1/2 means 1/2 of a tank Car B gives to Car A.
(1/2 a tank was all car B had.)
I think I made an error trying to
give info from my worksheet.
I posted in on my blog.
http://ragknot.blogspot.com/
it didn't say ALL the other cars needed to cross the desert so why not transfer the fuel from all the other cars to one single car and have that car travel the whole way from their starting point to deliver the mail
is there a link to the answer?
This post has been removed by the author.
Anon:
You can't put more than 100% in a tank. And you can't take gas cans or tow ropes, etc
All four cars drives drive to the 1/8 distance
All cars have 3/4 of tank, car 4 gives the other 3 cars a 1/4 tank each, that fills each tank.
The three remaining cars drive to the 1/4 distance
The three remaining cars have 3/4 of a tank each.
Car 3 gives 1/4 tank, to Cars 1 and 3. That fills them up. Car 3 is done.
Cars 1 and 2 drive to the 1/2 distance.
Cars 1 and 2 have 1/2 tank
Car 2 gives his half tank to Car 1.
Car 1 can drive the remaining 1/2 now.
Walk...
there is no pipes or rope so the easy answer is firstly you push the front car with the 1 behind hence not using ropes or pipe when reach half way the front car starts to drive as normal. making the full journey without any complication
If d is the distance one car can do with one full tank, then the maximum distance n cars can achieve by transferring petrol is ∑(i=1...n) d/i. If d = 1/2 (e.g. half the length of the desert), then three cars can achieve up to 1/2 + 1/4 + 1/6 = 11/12 < 1, four cars can achieve up to 1/2 + 1/4 + 1/6 + 1/8 = 25/24 > 1. So n = 4 is the minimum number of cars needed for the job.
Thought that might be interesting.
i just have a quick question for everyone who said they would transfer fuel from car to car, how are you going to do that when it says u have no canisters and how would u go about transferring the fuel? Im not saying your wrong or insulting you in any way im just curious.
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