## Thursday, May 6, 2010

### A Water Puzzle

This week is all about water in the Boston, MA area. A large pipe supplying drinking water to two million people burst open. While authorities redirected the water supply to come from the local reservoir, people were warned to use this replacement water for bathing but stick to bottled water for drinking. Imagine how fast water disappeared off the shelves of local stores.

This is a puzzle about one local store that ran out of bottled water very quickly, leaving only one large 12 gallon emergency barrel. Two customers grabbed this barrel at the same time and were contemplating how to divide it. The store didn't have any 6 gallon containers, but did have empty 8 gallon and 5 gallon containers. The customers thought for a while but then figured it out. Both went home with 6 gallons of water each. How did they do it?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Wang said...

Love these kinds of puzzles!

Pour the 12 gallon barrel into the 8 gallon barrel. You now have 8 gallons of water and 4 gallons of water.

12 (4 gallons)
8 (8 gallons)
5 (0 gallons)

Pour the 4 gallons of water into the 5 gallon barrel and then the 8 gallons of water to the 8 gallon barrel, finally, pouring the 4 gallons of water from the 5 gallon barrel to the 8 gallon barrel. (Switching the 8 and 4 gallons of water)

12 (8 gallons)
8 (4 gallons)
5 (0 gallons)

Pour the 8 gallons of water into the 5 gallon barrel

12 (3 gallons)
8 (4 gallons)
5 (5 gallons)

Pour the 5 gallons of water into the 8 gallon barrel, leaving 1 gallon in the 5 gallon barrel

12 (3 gallons)
8 (8 gallons)
5 (1 gallon)

Pour the 8 gallon barrel into the 12 gallon barrel.

12 (11 gallons)
8 (0 gallons)
5 (1 gallon)

Finally, pour the 1 gallon into the 8 gallon barrel, fill the 5 gallon barrel.

12 (6 gallons)
8 (1 gallon)
5 (5 gallons)

And then finally, fill the 8 gallon barrel with the 5 gallons of water.

12 (6 gallons)
8 (6 gallons)

Those customers must have been pretty strong to lift so many gallons of water!

Maria said...

Wow, Wang! This is very impressive.
It looks like it would take ten operations to perform this split. You explained it so thoroughly. But since you combined some of the steps, let me list them all using your methodology:
0)12(12) 8(0) 5(0)
1)12(4) 8(8) 5(0)
2)12(0) 8(8) 5(4)
3)12(8) 8(0) 5(4)
4)12(8) 8(4) 5(0)
5)12(3) 8(4) 5(5)
6)12(3) 8(8) 5(1)
7)12(11) 8(0) 5(1)
8)12(11) 8(1) 5(0)
9)12(6) 8(1) 5(5)
10)12(6) 8(6) 5(0)

A well-deserved puzzle point for Wang.
Now - offering two puzzle points for anyne who could make it in less than ten steps.

Lynnet said...

(the # in the () is how many gallons there are, the # out of the () is the # of gallons the container can hold, g=gallons)

You fill the 8g container from the 12g container=12(4g) 8(8g) 5(0g)

You then fill the 5g container from the 8g container=12(4g) 8(3g) 5(5g)

then you pour the 5g container into the 12g container=12(9g) 8(3g) 5(5g)

pour the 8g container into the 5g container = 12(9g) 8(0g) 5(3g)

pour the 12g container into the 8g container = 12(1g) 8(8g), 5(3g)

pour the 8g into the 5g = 12(1g), 8(6g), 5(5g)

pour the 5g back into the 12g = 12(6g), 8(6g), 5(0g)

one customer has the 12g container and the other has the 8g container.

Maria said...

Let me double-check it:
0)12(12) 8(0) 5(0)
1)12(4g) 8(8g) 5(0g)
2)12(4g) 8(3g) 5(5g)
3)12(9g) 8(3g) 5(0g) - you accidentally wrote 5(3g) here
4)12(9g) 8(0g) 5(3g)
5)12(1g) 8(8g), 5(3g)
6)12(1g), 8(6g), 5(5g)
7)12(6g), 8(6g), 5(0g)

Fantastic! Two promised puzzle-point for Lynnet. Welcome to the puzzle marathon! Three new puzzles are coming next Friday.

Tom said...

Fill the 8. (we're going for a couple of 3's, easy)
Pour 5 into a 5. (I assume there are plenty/many 5-gallon bottles here)
3 remain. Pour the 3 into some other 5.
Refill the 8 (with the 5 from line 2, and more from the barrel).
Again pour 5 into a 5 as in line 3; 3 remain, pour them into another 5.
Now you've got two 5-gallon bottles each with 3 gallons in them.
Send those home with one customer.
6 remain at the store, and the second customer can take them home as he/she chooses, in the barrel, or in two smaller containers, whatever.

Maria said...

Well, I did not mean that they have more than one of each 5 and 8 gallon containers, but why not consider it? Assume they found these in the recycling bins...
0)12(12) 8(0) 5(0)
1)12(4) 8(8) 5(0)
2)12(4) 8(3) 5(5)
3)12(4) 8(0) 5(5) 5(3)
4)12(4) 8(5) 5(0) 5(3)
5)12(1) 8(8) 5(0) 5(3)
6)12(1) 8(3) 5(5) 5(3)
7)12(1) 8(6) 5(5) 5(0)
8)1(6) 8(6) 5(0) 5(0)

Works well!
You are the same Tom, right? Tom that has 5 puzzle points already and now gained two more.