# 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

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

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My Books

“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444

“The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias” is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/

“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

“Math Puzzles Volume 2” is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/

“Math Puzzles Volume 3” is the third in the series. https://www.amazon.com/gp/product/1517596351/

“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/

“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/

source

Fahad Hashmi is one of the known Software Engineer and blogger likes to blog about design resources. He is passionate about collecting the awe-inspiring design tools, to help designers.He blogs only for Designers & Photographers.

### 32 thoughts on “The 3 Jug Riddle”

• September 27, 2017 at 1:44 pm

Is there an algorithm for solving this type of problem?

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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.

• September 27, 2017 at 1:44 pm

12 0 0
4 8 0
0 8 4
0 0 4
12 0 4
11 0 5
11 0 0
6 0 5

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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,

• September 27, 2017 at 1:44 pm

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.

• September 27, 2017 at 1:44 pm

Just say to the milkman "you need some milk"

• September 27, 2017 at 1:44 pm

so milk is blue? this world….

• September 27, 2017 at 1:44 pm

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)?

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

Darn! I misunderstood the question.

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

Wait is this the question from Die Hard?

• September 27, 2017 at 1:44 pm

Nah, i'd rather estimate

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

12 0 0
4 8 0
4 3 5
9 3 0
9 0 3
1 8 3
1 6 5

• September 27, 2017 at 1:44 pm

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.

• September 27, 2017 at 1:44 pm

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.

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

This was so complicated haha im just dumb

• September 27, 2017 at 1:44 pm

Easier solution: 4 steps
12 0 0 (initial)
8 0 5
8 5 0
12 1 0
12 6 0 (optional)

• September 27, 2017 at 1:44 pm

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

• September 27, 2017 at 1:44 pm

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.

• September 27, 2017 at 1:44 pm

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