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## Water and Vinegar

Posted by trickofmind on August 4, 2010 – 4:24 am

The old puzzle was you have one litre of water in one bucket and one litre of vinegar in another bucket. Take a spoonful of water from the first bucket and mix it thoroughly with the vinegar in the second. Now take a spoonful of the vinegar-water mixture in the second bucket and mix it back with the water in the first. Problem: does the first bucket have more vinegar or the second bucket more water? Solve it only if you can get at the most elegant solution with no math involved at all.

This post is under “Logic, Tom” and has 12 respond so far.

### 12 Responds so far- Add one»

1. 1. Jay Said：

The second bucket has more water.

The water put into the vinegar was pure, whereas the vinegar put into the first bucket is contaminated with water.

2. 2. Karl Sharman Said：

If the answer is the same as it would be for wine and water… then I know the answer from the old ToM, which is………

3. 3. Kevin Said：

I like Jays answer except for the fact that once you remove a spoonfull of water from the first bucket you are no longer dealing with a “Full” liter. I think because of the reduction of the amount of liquid in the first bucket and because of the increase of the amount of liquid in the second bucket that they might actually be more to the question than the simple answer. To answer I would take it to extreme case where your spoon size is equivalent to 1 liter. If I took a spoonfull of water (1 liter) and added it to the vinegar it would basically be mixing equal amounts. Then it is obvious when I take a spoonful back to the original bucket that each bucket has equal amounts of water and vinegar in each bucket.
Now lets reduce the size of the spoon. If the spoon were only half a liter in size and I pulled a spoon from the left (water bucket)I would have remaining .5 liters of straight water in left bucket and now 2 parts vinegar to 1 part water mixture in the right bucket. Returning half a liter from right bucket to the left bucket (remember we now have 1/2 liter sized spoon) of this to the left bucket does (2) things. First it leaves the right bucket still as 2 parts vinegar to 1 part water. It also brings 2 parts of vinegar and 1 part of water to the original left bucket (1/2 liter). Since the spoon and the bucket of water are the same size (1/2 liter) we can treat this as a simple additive effect. We would be adding 1 part of water and 2 parts of vinegar (total 3) to the left bucket which to keep things equivalent (1/2 liter and 1/2 liter) is starting as 3 parts of water. This additive effect results in 2 parts vinegar and 4 parts water going into the left bucket. Now it becomes easy to see that the left bucket and the right bucket have the same correspondig mixtures and therefore they are equivalent in that the same ratio exists. Answer Neither the water bucket nor the vinegar bucket have more of the opposition liquid in them.
Incidently you can visualize the same thing if the spoon size becomes miniscule. Mentally imagine that the spoon is actually 0. In this case there is no mixing of the two liquids and the equivalent ratios will still stay intact.

4. 4. Chris Said：

Kevin has the correct result. The reason is very simple

5. 5. Jay Said：

Agreed. Nice one Kevin. I tried to be a little too simple there. ;o)

6. 6. Chris Said：

After the exchange, the volume of the mixtures in each container, must be the same as before the exchange. The overall amount of water that has been removed from the water container, must have been replaced with the same amount of vinegar, and vice-versa.

The absolute amount of contaminant in each container is the same.

It doesn’t matter if the mixtures are stirred thoroughly or not.

7. 7. steve Said：

but vinegar is 95% water and 5% acetic acid (avg)
it ranges from 4 to 8% and as high as 18% for pickling.

8. 8. Jeffrey Said：

Ummm first of all first have equal parts. So mixing both dusch err uhh, wow what a brain twister. The real question is obviously if you can answer the question you are probably about 89 on an IQ analysis. For the people that answer this are they any smarter?

9. 9. Dr. Masood Anwar Said：

vinegar will be more than the water.

10. 10. ankush Said：

second bucket has more water

11. 11. Stefan Said：

If you scoop out the Vinegar-Water mixture all you get is vinegar. [Vinegar floats on top of water]. Bucket a has the same amount of vinegar as the second one Water.

12. 12. Chris Said：

Hi Stefan. Vinegar is compeletely miscible with water. But the question isn’t meant to be a trick one. You are supposed to regard the water and vinegar as two distinct liquids that are logically distinguishable.

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