Gallon Puzzle

[pdurrant]

You need to measure out exactly one gallon (8 pints) of water. But you only have a 7 pint jug (currently empty), a 3 pint jug (currently empty), and a
two gallon (16 pint) bucket (very nearly full of water).

None of the containers have subdivisions - you can only measure exactly by filling one up to the brim.

You may pour water down the drain, but water poured away cannot be recovered. You don't have any supply of water except the very nearly full two gallon bucket.

How can you end up with exactly one gallon of water? You may assume that you have very steady hands.

Answers in spoiler tags please.

[Javed]

Think I got it!

Spoiler:

Pour from the 16 pint container into the 7 pint container until full.

Pour from that 7 pint container into the 3 pint container until the 3pint container is fulll.

Discard what is in the 3.

Pour the remainder of the 7 pint container which is 4 pints back into the 16pint container.

Pour from the 16pint container into the 7 pint container until full.

Pour from the 7 pint container into the 3 pint container until full.

Discard what is in the 3.

Pour the remainder of the 7 pint container into the 16 pint container.

The 16 pint container now has 8 pints (one gallon).

[GeoffC]

Interesting, if one uses the forumspy - it ignores the spoiler ....

[Javed]

Originally Posted by GeoffC

Interesting, if one uses the forumspy - it ignores the spoiler ....

[Javed]

Can the forum spy see the next word after this...ok it is more than one word.

Hmm, had a look. The spy can see white text....amazing turns it to black text!

[pdurrant]

Originally Posted by Javed

Think I got it!

Spoiler:

Pour from the 16 pint container into the 7 pint container until full.

Pour from that 7 pint container into the 3 pint container until the 3pint container is fulll.

Discard what is in the 3.

Pour the remainder of the 7 pint container which is 4 pints back into the 16pint container.

Pour from the 16pint container into the 7 pint container until full.

Pour from the 7 pint container into the 3 pint container until full.

Discard what is in the 3.

Pour the remainder of the 7 pint container into the 16 pint container.

The 16 pint container now has 8 pints (one gallon).

Sorry, not right. You have a couple of errors.
The first is assuming that the 16 pint bucket is full. It isn't. It's only nearly full.
The second is discarding water from the wrong container — you'd end up with 10 pints.

I can see what you're trying to do, but even if you'd discarded the right container, it still doesn't work, because you don't start off with 16 pints.

Try again!

[pdurrant]

Originally Posted by GeoffC

Interesting, if one uses the forumspy - it ignores the spoiler ....

Sounds like a bug. But not to worry in this instance — it isn't the right answer.

[dsvick]

Here is my effort

Spoiler:

Fill both the 3 and the 7 pint containers, discard what is left in the bucket.
Pour the two containers back into the bucket for a total of 10 pints.

Fill the 3 pint to the top and pour it into the 7 pint, do this twice.
There is now 6 pints in the 7 pint container and 4 pints in the bucket

Fill the three pint container again, pour from there into the 7 pint container until it is full, this will leave 2 pints in the 3 pint container.

Dump those 2 pints, pour the 7 pints from the large container into the bucket that had 1 pint left - it now has 8 pints in it.

[pdurrant]

Originally Posted by dsvick

Here is my effort

Spoiler:

Fill both the 3 and the 7 pint containers, discard what is left in the bucket.
Pour the two containers back into the bucket for a total of 10 pints.

Fill the 3 pint to the top and pour it into the 7 pint, do this twice.
There is now 6 pints in the 7 pint container and 4 pints in the bucket

Fill the three pint container again, pour from there into the 7 pint container until it is full, this will leave 2 pints in the 3 pint container.

Dump those 2 pints, pour the 7 pints from the large container into the bucket that had 1 pint left - it now has 8 pints in it.

Very good! That's a right answer!

For bonus points, work out how to get a gallon of water without having the two gallon container, just a tap (faucet) from which you can get water to fill the 3 or 7 pint jugs...

[Javed]

I tipped the wrong one out last time. OK. I think I have it now.......

(no peeping Geoff!)

Spoiler:

Pour from the 16 pint container into the 7 pint container until full.

Pour from that 7 pint container into the 3 pint container until the 3pint container is fulll.

Discard what is in the 7.

Pour the remainder of the 3 pint container which is 3 pints back into the 16pint container.

Pour from the 16pint container into the 7 pint container until full.

Pour from the 7 pint container into the 3 pint container until full.

Discard what is in the 7 pint container.

Pour the remainder of the 3 pint container into the 16 pint container.

The 16 pint container now has 8 pints (one gallon).

[pdurrant]

Originally Posted by Javed

I tipped the wrong one out last time. OK. I think I have it now.......

(no peeping Geoff!)

Spoiler:

Pour from the 16 pint container into the 7 pint container until full.

Pour from that 7 pint container into the 3 pint container until the 3pint container is fulll.

Discard what is in the 7.

Pour the remainder of the 3 pint container which is 3 pints back into the 16pint container.

Pour from the 16pint container into the 7 pint container until full.

Pour from the 7 pint container into the 3 pint container until full.

Discard what is in the 7 pint container.

Pour the remainder of the 3 pint container into the 16 pint container.

The 16 pint container now has 8 pints (one gallon).

Alas, no. Your method gives you a little less than a gallon, as the two gallon container starts off "very nearly full" not full.

Have another go!

[dsvick]

Originally Posted by pdurrant

Very good! That's a right answer!

For bonus points, work out how to get a gallon of water without having the two gallon container, just a tap (faucet) from which you can get water to fill the 3 or 7 pint jugs...

That's easy, just work back wards from the first solution

Spoiler:

Fill the 7 all the way and dump it into the 3 pint container, then dump the 3 out - do this twice, leaving 1 pint in the 7 pint container.

Dump that pint into the 3 pinter, and then fill the seven back up.

[omk3]

Here's mine:

Spoiler:

Visually:


16...0...0
..-->.....
.9...7...0
......-->.
.9...4...3
..<------.
12...4...0
......-->.
12...1...3
..<------.
15...1...0
......-->.
15...0...1
..-->.....
.8...7...1

Because the first 8 is probably not exact, pour it out and pour in the 7+1.
Done.

[dsvick]

Originally Posted by pdurrant

Very good! That's a right answer!

For bonus points, work out how to get a gallon of water without having the two gallon container, just a tap (faucet) from which you can get water to fill the 3 or 7 pint jugs...

Originally Posted by dsvick

That's easy, just work back wards from the first solution

Spoiler:

Fill the 7 all the way and dump it into the 3 pint container, then dump the 3 out - do this twice, leaving 1 pint in the 7 pint container.

Dump that pint into the 3 pinter, and then fill the seven back up.

And that would also be another solution for the original as well substituting the 2 gal container for hose.

[pdurrant]

Originally Posted by omk3

Here's mine:

Spoiler:

Visually:


16...0...0
..-->.....
.9...7...0
......-->.
.9...4...3
..<------.
12...4...0
......-->.
12...1...3
..<------.
15...1...0
......-->.
15...0...1
..-->.....
.8...7...1

Because the first 8 is probably not exact, pour it out and pour in the 7+1.
Done.

Very nice. And yes, that's also a right answer.