# The 3 Jug Riddle

You have a full 12 liter jug and empty 5 and 8 liter jugs. Can you measure exactly 6 liters? This problem dates to 1484 and was posed in the context of a milkman making a home delivery to a customer. The story goes this riddle so delighted Simeon Denis Poisson as a young boy that it was one reason he pursued mathematics.

Can you measure all whole amounts from 1 to 12? Answer in blog post: http://mindyourdecisions.com/blog/2015/09/13/the-3-jug-riddle-sunday-puzzle/#.VfXYpRFVhBc

There’s a similar puzzle from the movie “Die Hard 3.” How can you measure 4 liters from 3 and 5 gallon jugs? Here’s my video on that: https://www.youtube.com/watch?v=KfNRArPXCjw

The source of this puzzle and its history is from “Famous Puzzles of Great Mathematicians”: http://amzn.to/1EYVCJb

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source

Is there an algorithm for solving this type of problem?

I found

Start 12 0 0

1 4 8 0

2 4 3 5

3 9 3 0

4 9 0 3

5 1 8 3

6 1 6 5

7 6 6 0

8 from 12 into 8 (4/8/0)

5 from 8 into 5 (4/3/5)

5 from 5 into 12 (9/3/0)

3 from 8 into 5 (9/0/3)

8 from 12 into 8 (1/8/3)

2 from 8 into 5 (1/6/5)

5 from 5 into 12 (6/6/0)

Ta-da.

How about

12 0 0

4 8 0

0 8 4

0 0 4

12 0 4

11 0 5

11 0 0

6 0 5

i did : 12-0-0; 4-8-0;4-3-5; 9-3-0;9-0-3; 1-8-3; 1-6-5;6-6-0

Hard Way

Step 1: Fill 8 Litre container

Step 2: Empty 8 Litre into 5 Litre container. The 8 Litre container has 3 Litres and the 5 Litre container is full.

Step 3: Pour the 3 Litres of milk into the 6 Litre container that you have at the side.

Step 4: Repeat Steps 1 through 3, but first pour the 9 Litres of milk that you still have to use back into the 12 Litre container. The 6 Litre container you have at the side is properly filled and the remaining containers have a total of 6 Litres of milk for you.

Easy Way

Step 1: Stop being lazy and find a 6 Litre container that you used for somebody else.

Step 2: Pour 6 Litres of milk from the 12 Litre container to the 6 Litre container. Both the 12 Litre container and the 6 Litre container have 6 Litres. 6 for the customer and 6 for you,

I was presented this problem by our teacher in 3rd grade (mainly to shut me up for a while). Took me a few minutes to solve it. Teacher was frustrated. Several weeks later she went on maternal leave (not my fault though). She came back when I left school and my mom keeps saying the waited until I was gone.

Just say to the milkman "you need some milk"

so milk is blue? this world….

Why not just tip the 12 liter jug 1/2 way (so milk touches top right edge & bottom left) into 8 liter container (and keep the 5 liter totally clean)?

The solution was nothing but hit and trial, Can someone suggest some mathematical logic to explain why we took each step?

Darn! I misunderstood the question.

Couldn't he just pour into the 8 liter jug until both jugs were even? Not as exact or mathematical as your answer but I feel like the problem was still solve

they could've just filled the 8-liter jug until the milk levels are equal in the 8 and 12 liter jugs

A =12 | B = 0 | C = 0

Pour A into B

A = 4 | B = 8 | C = 0

Pour B into C

A = 4 | B = 3 | C = 5

Pour C into A

A = 9 | B = 3 | C = 0

Pour B into C

A = 9 | B = 0 | C = 3

Pour A into B

A = 1 | B = 8 | C = 3

Pour B into C

A = 1 | B = 6 | C = 5

Pour C into A

A = 6 | B = 6 | C = 0

Pour back and forth between the first two containers till the levels are exactly even at 6 liters each.

Wait is this the question from Die Hard?

Nah, i'd rather estimate

I havent watched the video yet. This is my solution.

1) fill 8 liter jug

2) pour 8 liter jug into 12 liter jug.

3) fill 5 liter jug.

4) pour 5 liter jug into 12 liter jug til 12 is full. You should have 1 liter left in the 5 liter jug.

5) pour the remaining 1 liter in the 5 liter jug into the 8 liter jug.

6) fill the 5 liter jug again, using the 12 liter jug or whatever.

7) pour the 5 liter jug into the 8 liter jug.

8) 8 liter jug now holds 6 liters

12 0 0

4 8 0

4 3 5

9 3 0

9 0 3

1 8 3

1 6 5

i'm going to pour what looks like 3/4 full into the 8 liter jug – i might measure it with a string of the same length as the jug height (folded twice) down from the top, but i'm willing to gamble that i'll be closer to correct than trying to fill all the jugs twice over without spilling any.

Three clear jugs with different volumes, that have the same diameter? First, let's make an assumption: the milk goes all the way to the top of the 12-liter jug with no air space above it. A mathematician moonlighting as a milkman might do all this pouring. A real milkman would pick up a page from the daily newspaper, cut it to the height of the 12-liter jug, then fold it in half and use it to mark the customer's 8-liter jug at the 6-liter mark.

there is another solution just pour the 12 liter to both 5 and 8 liter jug (i know it isnt full), then measure the height of the 12 liter give it a sign and pour milk until it reaches the sign

Got another sequence. Maybe I looked at it wrong, to tired to try again.

12 – 0 – 0

4 – 8 – 0

8 – 4 – 0

3 – 4 – 5

3 – 8 – 1

11 – 0 – 1

11 – 1 – 0

6 – 1 – 5

6 – 6 – 0

Duh, fill up the 8 liter, put it in the 5th one with 3 liters left, and repeat again, then you have 6, boom done, I did is before seeing the answer

Edit, I was sort of right

This was so complicated haha im just dumb

Easier solution: 4 steps

12 0 0 (initial)

8 0 5

8 5 0

12 1 0

12 1 5 (answer)

12 6 0 (optional)

Havent watched yet or looked at comment,

1) pour 12L into 8L (4L left in 12L)

2) pour 8L into 5L (3L left in 8L)

3) pour 5L into 12L (9L in the 12L)

4) pour 8L (with 3L in it) into the 5L (3L in the 5L)

5) pour 12L into 8L (1L left in 12L)

6) pour 8L into 5L (6L in the 8L jar) (5L in 5L jar)

7) pour 5L into 12L jar

8) customer takes their jars and milkman takes his 12L jar home

9) simple

fill the 8 liters from the 12 liters. fill the 5 liters from the 8 liter. the 8 liters there should be 3 liters left in the 8 liters jug. Get another 8 liters jug. do the same again. leave the 2 8 liter jugs at the costumers place, pur the rest back to the 12 liters jug and leave with the half empty 12 liters jug.

so easy lol

put a 12 in 8

put the 8 in 5

there should be a 3 in an 8

put the 5 in the 12

put the 3 in the 5

put the 9 (from 12) into 8

12 has 1

fill the 5 from the 8

put the 5 in the 12

12 has 6, 8 has 6

done and won

The question I have is "How does the customer know he received exactly 6 liters?"