Two glasses, two transfers and a seemingly very simple question. It is one of those riddles that invite you to calculate right away, although the decisive factor does not always come in the longest count.
Water and wine
Riddle statement
You have a glass full of water and another full of wine, both with the same amount.
You transfer a tablespoon of water to the glass of wine and mix.
Then you pour a tablespoon of that mixture back into the glass of water.
What's more at the end: water in the glass of wine, or wine in the glass of water?
Show solution
Solution
Answer: There is exactly the same amount.
Explanation:
After the first transfer, the glass of wine contains a little water. After the second, the glass of water receives a spoonful of that mixture, which includes some wine.
The cleanest way to look at it is not by calculating proportions but by looking at what is conserved:
In the end, both glasses once again have exactly the same volume as at the beginning.
All the liquid that came out of one glass was replaced by the same amount from the another.
This means that each spoonful of water that ended up in the glass of wine displaced, by necessity, a spoonful of wine into the glass of water. The two quantities are equal by construction, not by chance.