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anujkumar
October 2nd, 2003, 01:27 PM
You have a car with a tank capacity of exactly one gallon, So at no point of time is it possible to have more than 1 gallon of fuel, but you can empty it (if you want) and place the fuel on the roadside for future use. Car consume 1 gallon per mile. You want to reach a place 2 mile down a stright road from a petrol pump.

What is the least amount of fuel you would be able to do it and how?

bnashier
October 2nd, 2003, 07:23 PM
The answer is 11 gallons. of course, if you have a container to store the petrol on the way, then why not carry an extra gallon in the car and you will be fine in two just gallons. But the intent of your question is mathematical and then it is fun !

Explanation. You need to have full tank (1 gallon) 1-mile mark. You transport 5 gallons at 1/4th mile from petrol pump. You will leave 1/2 gallon at a time. In doing so, you consume 5 gallons. Fill the 11th gallon and you are now with 5.75 gallons at 1/4th mile. Transpost at 1/2 mile and you will be with 3 gallons. Now at 3/4th mile and you are with 1.75 gallons. Finally at 1-mile post and you have a full tank.

drnchaudhry
October 2nd, 2003, 07:29 PM
No need of fuel at all!
Car will roll down a straight road with its engine off
It will need a push up to roll down and breaks later on.
Enjoy the ride!

bnashier
October 2nd, 2003, 07:58 PM
Narender Ji:

I think it is a great idea ! I like it and that is what you do with a car that can hold only one gallon of fuel.


Dr. Narender Dudee (Oct 02, 2003 09:59 a.m.):
No need of fuel at all!
Car will roll down a straight road with its engine off
It will need a push up to roll down and breaks later on.
Enjoy the ride!

anujkumar
October 2nd, 2003, 09:43 PM
It's not correct Nashier Sir, 11 Gallon for 2 mile....Your car is consuming too much. One can do better.
Anuj

Budh Nashier (Oct 02, 2003 09:53 a.m.):
The answer is 11 gallons. of course, if you have a container to store the petrol on the way, then why not carry an extra gallon in the car and you will be fine in two just gallons. But the intent of your question is mathematical and then it is fun !

Explanation. You need to have full tank (1 gallon) 1-mile mark. You transport 5 gallons at 1/4th mile from petrol pump. You will leave 1/2 gallon at a time. In doing so, you consume 5 gallons. Fill the 11th gallon and you are now with 5.75 gallons at 1/4th mile. Transpost at 1/2 mile and you will be with 3 gallons. Now at 3/4th mile and you are with 1.75 gallons. Finally at 1-mile post and you have a full tank.

anujkumar
October 2nd, 2003, 09:51 PM
Hint: What if you have to reach just 4/3 miles.

bnashier
October 2nd, 2003, 10:44 PM
Well, I did not write any algorithm. I infer that you transport the petrol at varoius junctures so that the tank is emply (to minimize consumption) when you get back. And 1/2 gallon at a time fits the bill. Perhaps there is better algorithm.


Anuj Kumar (Oct 02, 2003 12:13 p.m.):
It's not correct Nashier Sir, 11 Gallon for 2 mile....Your car is consuming too much. One can do better.
Anuj

Budh Nashier (Oct 02, 2003 09:53 a.m.):
The answer is 11 gallons. of course, if you have a container to store the petrol on the way, then why not carry an extra gallon in the car and you will be fine in two just gallons. But the intent of your question is mathematical and then it is fun !

Explanation. You need to have full tank (1 gallon) 1-mile mark. You transport 5 gallons at 1/4th mile from petrol pump. You will leave 1/2 gallon at a time. In doing so, you consume 5 gallons. Fill the 11th gallon and you are now with 5.75 gallons at 1/4th mile. Transpost at 1/2 mile and you will be with 3 gallons. Now at 3/4th mile and you are with 1.75 gallons. Finally at 1-mile post and you have a full tank.

anujkumar
October 4th, 2003, 03:55 AM
OK Great, Nashier Sir and Dudee Sir, both of get full points for correct answers in their own sense.
Anuj

rsdalal
October 4th, 2003, 07:50 AM
Anuj How about 40 Gallans.

Make 24 trips to 1/3 miles mark and empty 1/3 tank at the end and come back so 2/3 tank used in going and comming back, 1/3 stored at 1/3 mile from Gas station. Total stored = 8 gallons after 24 trips.

Now make 12 more trips from gas station to 2/3 mile mark and on the way collect 1/3 tank from 1/3 mile and empty 1/3 Gallon at 2/3 mile point and collect 1/3 Gallon more while back, so that when you reach Gas station you will have empty tank. So in 12 trips total collected Gallons will be 4 Gallons at 2/3 mile mark.

Now make 3 more trips from Gas station with full tank to 1 mile mark and on the way collect 2/3 tank from 2/3 mile mark and emty 1/3 tank at 1 mile mark.While back you will collect 2/3 tank again from the 2/3 mile mark and you will be able to reach Gas station with emty tank.

And now the final trip from Full tank from Gas station to 1 mile mark, where 1 Gallon is waiting for you, whith that you will be able to reach 2 mile marke.

Total consumption will be
24 Gallon
12 Gallon
3 Gallon
1 Gallon
=40Gallon

rsdalal
October 4th, 2003, 09:38 AM
40 Gallon is not the efficient answer, I did not read Mr. Nashier's answer before, as it is more efficient, but looks like Anuj have even better...

anujkumar
October 4th, 2003, 11:00 AM
The best answer is ~7.6 Let's make it in 8 gallon!
1) Make 7 trips to 1/15 mark. Take 8 gallon, Consume 1 gallon and deposit 7. (Trip always end at mark and that mark becomes petrol pump for future)
2) Make 6 trips to 1/13 mark (from previous mark). Consume 1 gallon and deposit 6.
3)make 5 trips to 1/11 farther mark. Consume 1 gallon and deposit 5.
3) Make 4 trips to 1/9 farther mark. Consume 1 and deposit 4.
4) Make 3 trips to 1/7 farther mark. Consume 1 and deposit 3.
5) Make 2 trips to 1/5 farther mark. Consume 1 and deposit 2.
6)Make 1 trip to 1/3 farther mark. Consume 1 and depsit 1

Now if you add up the distance we have travelled (1/15+1/13+1/11+...+1/5+1/3). It is greater than 1 and we have 1 gallon and we are threre ready to shoot to 2 mile (well slightly beyond ..that makes answer less than 7).

Both Dalal Sir and Nashier Sir were in right direction. Both would have reached it if given couple of days.

But beauty of the solution is worth noting. You may trick your interested friends with it.

bnashier
October 4th, 2003, 11:26 PM
Very good.

The crux seems to be to divide the passage in such a way that you consume 1 gallon in transport in each segment. There should be an equation now to show that this gives the optimal result - like a bell-shaped distribution.


Anuj Kumar (Oct 04, 2003 03:40 a.m.):
The best answer is ~7.6 Let's make it in 8 gallon!
1) Make 7 trips to 1/15 mark. Take 8 gallon, Consume 1 gallon and deposit 7. (Trip always end at mark and that mark becomes petrol pump for future)
2) Make 6 trips to 1/13 mark (from previous mark). Consume 1 gallon and deposit 6.
3)make 5 trips to 1/11 farther mark. Consume 1 gallon and deposit 5.
3) Make 4 trips to 1/9 farther mark. Consume 1 and deposit 4.
4) Make 3 trips to 1/7 farther mark. Consume 1 and deposit 3.
5) Make 2 trips to 1/5 farther mark. Consume 1 and deposit 2.
6)Make 1 trip to 1/3 farther mark. Consume 1 and depsit 1

Now if you add up the distance we have travelled (1/15+1/13+1/11+...+1/5+1/3). It is greater than 1 and we have 1 gallon and we are threre ready to shoot to 2 mile (well slightly beyond ..that makes answer less than 7).

Both Dalal Sir and Nashier Sir were in right direction. Both would have reached it if given couple of days.

But beauty of the solution is worth noting. You may trick your interested friends with it.