### Brain Teasers

# The Dairy Farmer

A dairy farmer had 54 litres of milk in three churns. He wanted to make sure each churn contained 18 litres.

First, he poured 1/4 of the first churn into the second churn. Then he poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.

How many litres did each churn contain before he started pouring?

First, he poured 1/4 of the first churn into the second churn. Then he poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.

How many litres did each churn contain before he started pouring?

### Answer

12, 33 and 9 litres respectivelyHide Answer Show Answer

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## Comments

Good teaser, however it says the farmer "wants" 18 in each and then he goes through the process. I was not sure whether at the end of his pours he for sure had 18 in each. I assumed this to be true and solved the teaser. However, if at the end there's 16, 18, 20 then a different answer can be found, and the farmer would need to keep pouring.

Just think it needs to be better worded.

Just think it needs to be better worded.

That was really good. It took me a lot of thinking to get it, but I finally did. Great job!

Interesting puzzle, worth the effort, just had to find the right approach to get started. Oh, to think I was about to give up on it at first.

I agree with smek, but I also just assumed he ended with the correct amount in each and worked it out. Apart from the wording, great teaser.

Nice one. Agree with other comments that it should be explicitly said that he ends up with 18L in each

It was a good, hard riddle.

love these math teasers. took me a couple minutes, though.

I've never been a Math person...

Brilliant, brilliant, brilliant

Nov 11, 2006

I would not rate this as a great teaser.

x, y, z

3x/4, y + x/4, z

3x/4, y/2 + x/8, z + y/2 + x/8

3x/4 + z/3 + y/6 + x/24, y/2 + x/8, 2z/3 + y/3 + x/12

3x/4 + 9 = 18 => x = 12;

y/2 + 12/8 = 18 => y = 33;

2z/3 + 33/3 + 12/12 = 18 => z = 9;

x, y, z

3x/4, y + x/4, z

3x/4, y/2 + x/8, z + y/2 + x/8

3x/4 + z/3 + y/6 + x/24, y/2 + x/8, 2z/3 + y/3 + x/12

3x/4 + 9 = 18 => x = 12;

y/2 + 12/8 = 18 => y = 33;

2z/3 + 33/3 + 12/12 = 18 => z = 9;

XIEXIE NI!!! THANK YOU!!!

NOT TOO DIFFICULT, BUT FOR ONCE, I HAD TO USE MY BRAIN FOR MORE THAN A FEW SECONDS.

"PLEASE" SEND SOME MORE.

NOT TOO DIFFICULT, BUT FOR ONCE, I HAD TO USE MY BRAIN FOR MORE THAN A FEW SECONDS.

"PLEASE" SEND SOME MORE.

if youre good at math.it was a good exercise..but for the normal joe it was probbably to hard..

Math is not my strong suit, so I'll have to take your word for it. Give me language teasers any time!!

Great Teaser! I got it on my first try!

Good teaser. I think the wording "make sure" concludes that all end with 18L each. I'm to sure why the farmer didn't just pour enough from 33 into each, but then we wouldn't have a teaser would we? Thanks!

My brain hurts.

I am not a Math Person!!

A fantastic teaser! The teaser is great, but the wording can lead to many pieces of criticism. Bring some more mah teasers, forward. I believe many people can and will enjoy them!

Maybe it's because I enjoy language teasers more but I also was confused at the wording.

This wasn't my favorite teaser ever. Finding the answer was easy, and there was terrible wording!

It was a little tedious, but a nice test of high school algebra. I wish the teaser wasn't so deterministic, though (the chosen values are simply to make the teaser "difficult", rather than for any other purpose).

I loved this teaser b/c I love math. I was very fun and not really to hard, just tedious. I agree with the person that said you had to find a starting point. loved it

Jan 31, 2007

If he poured 1/2 out of the second churn to get 18 litres doesn't that mean there was 36 litres in there?

I'm not very good at math so I think I'm confused

I'm not very good at math so I think I'm confused

Good math teaser but I really had to work at it!! Good job!!

Rwortley there were 36 litres in the 2nd AFTER it received 3 or 1/4 of the 12 litres from the 1st pour - which means it had 33 litres before the pouring began. The question seemed like it was worded fine to me. The teaser is a math teaser so wording should not be considered a stumblingblock. Off with all your commenting heads!

Great teaser!!

Great teaser!!

good, but i did this problem in math class last week

Good riddle. I AM a math person!

I don't do math - I'm a word person

Jan 31, 2007

Thanks jacstop now I can understand the answer, but I'm still fuzzy on how to get there.

Add me to the ranks of 'average joes', and thus I didn't get it. Algebraic formulas stymied me in my younger days, and my short term memory is fast disappearing, so I'm still stymied. Enjoyed seeing that IM liked it. Will look at it again in the morning and see if my brain does better when it's fresh!

Wow, that was awesome!! But I must confess that I am a math-head.

I've never seen a teaser like that before -- but never browsed the Math category because I was sure I'd have too much fun and not be able to drag myself away (much like I experienced with the trivia quizzes today when I learned of them!)

Thanks for the great teaser!

I've never seen a teaser like that before -- but never browsed the Math category because I was sure I'd have too much fun and not be able to drag myself away (much like I experienced with the trivia quizzes today when I learned of them!)

Thanks for the great teaser!

Funny how I like doing math when I've taken a class in it but have never considered it "fun". I'm glad however that it satisfied a need for those who do!

it took me a whilee but i got it. im happy.

Easy peasy lemon squeezy Good one and thanks.

Thanks!

What fun. I enjoyed that one, took some work but that is what this is all about.

What fun. I enjoyed that one, took some work but that is what this is all about.

Feb 01, 2007

Just need to get the visual right. Then it just flows.

Very nice teaser. Fairly easy to do in my head, but quite entertaining nonetheless.

I don't understand all the problems with the wording. Seemed pretty clear to me.

Before each pour:

Third = 3/2 x 18 = 27

Second = 2/1 x 18 = 36

First = 4/3 x (18 - 1/3 x 27) = 4/3 x 9 = 12

Starting:

Third = 27 - 1/2 x 36 = 9

Second = 36 - 1/4 x 12 = 33

First = 12

I don't understand all the problems with the wording. Seemed pretty clear to me.

Before each pour:

Third = 3/2 x 18 = 27

Second = 2/1 x 18 = 36

First = 4/3 x (18 - 1/3 x 27) = 4/3 x 9 = 12

Starting:

Third = 27 - 1/2 x 36 = 9

Second = 36 - 1/4 x 12 = 33

First = 12

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