The water puzzle from Die Hard III

[pokerfan]

To stop a bomb going off, McClane and Zeus have to measure out exactly four gallons of water from a fountain using a three gallon jug and a five gallon jug.

So how do you do it? No fair googling.

What's the most efficient method? I got it down to eight steps, counting filling, transferring and emptying as individual steps.

[Orrex]

1. Duh. Fill each one half way!

Seriously, here goes:

Jug A is the 3-gallon; Jug B is the 5-gallon.

1. Fill Jug A to the top
2. Pour all of Jug A into Jug B
3. Fill Jug A to the top
4. Using Jug A, fill Jug B to the top (leaving one gallon in Jug A)
5. Dump out all of Jug B
6. Pour the remaining one gallon from Jug A into Jug B
7. Fill Jug A to the top
8. Pour all of Jug A into Jug B. That's four gallons.

Eight steps, just like you. I guess we're some kinda geniuses!

[DarkTirade]

2. There's also another way if my logic is working.

1. Fill jug B to the top.
2. Pour into jug A. You now have three gallons in A and two in B.
3. Dump out jug A.
4. Pour remainder in jug B into jug A. Jug A has two gallons with room for one more.
5. Fill jug B.
6. Pour jug B into jug A. (don't spill any. :) )
You now have four gallons in jug B.

[pokerfan]

3. Looks good to me

Six steps. Well done.

[DarkTirade]

4. Phew. I was worried that I screwed up a step or two there.

I'd hate to look stupid in front of everybody. Or worse, have a bomb go off in my face. Then I'd look REALLY stupid. :P

[Orrex]

7. Doh! I concede that your logic is parsimoniouser!

But if you need to get three cannibals and three missionaries across the river, I'm your guy.

[DarkTirade]

8. I can do that too.

But if I do it, you'll end up with three missionaries inside three cannibals... :P

[Orrex]

10. Yikes! I'd hate to be in *that* missionary's position

So to speak...

[Dr. Strange]

5. Let us extend this problem, shall we?

What amounts can you get using these two containers?

Three, obviously: just fill the three gallon jug.
Five: just fill the five gallon jug.
Bruce Willis already did four.

What other amounts can you make?

What if the two containers were six and eight gallon jugs? What amounts could you make then?

[Orrex]

6. Ooo! Fun!

Two gallons is easy:

Fill the five-gallon jug and pour it into the three-gallon; the remainder is two gallons


One gallon?
Fill the three-gallon;
Pour it into the five;
Fill the three-gallon again;
Pour it into the five;
The remainder in the three-gallon is one gallon

Six and eight? I'll need to think about that. Maybe in the sequel...

[Dr. Strange]

11. I'll give you a hint: all (integer) amounts between 0 and 8 can be made.

Okay, that was more the answer than a hint...

Now, how about the 6- and 8-gallon jugs?

[Kutjara]

9. Without reading anyone else's answers:

1. Fill five gallon jug
2. Fill three gallon jug from five gallon jug, leaving two gallons in five gallon jug
3. Empty three gallon jug
4. Empty five gallon jug into three gallon jug
5. Fill five gallon jug
6. Pour one gallon from five gallon jug into three gallon jug, filling it.

There will now be four gallons in the five gallon jug.

[AllegroRondo]

14. beat me to it!

well done

[_testify_]

12. Here.

1. Fill 3 gallon jug.
2. Pour into 5 gallon jug.
3. Fill 3 gallon jug again.
4. Pour into 5 gallon jug, 1 gallon remains in 3 gallon jug.
5. Dump 5 gallon jug.
6. Pour 1 leftover gallon from step 4 into 5 gallon jug.
7. Fill 3 gallon jug again.
8. Pour into 5 gallon jug, you now have 4 gallons in the 5 gallon jug!

[AllegroRondo]

13. here you go, in 6 steps

1. fill 5 gallon
2. pour contents of 5 gal into 3 gal
3. empty 3 gal
4. pour remaining 2 gal from 5 into 3
5. fill 5 gal again
6. pour from 5 into 3 until full. this only takes one gallon, leaving 4 in the 5 gallon bucket.

[Rabrrrrrr]

15. I can do it in one step: Call your head butler and have him tell the cooper to make a 4 gal barrel

and bring it to you, already filled with water.

And have him get a couple bottles of '45 Dom Perignon from the steward, as well, and bring them with a couple glasses to celebrate.

[jmowreader]

16. You CAN'T do it, and here's why

Those jugs hold more than the stated amount--probably a quart more.

The only way you could do this is to get the jugs prefilled with their stated amounts, so you could mark the three-gallon and five-gallon increments. Then it's easy--follow the instructions posted about nine times in this thread already.