In the wine/water mixing problem , one starts with two barrels, one holds the wine and another the same water volume. A cup of wine is taken from the wine barrel and added to the water. A cup of wine/water mixture is then returned to the wine barrel, so the volume in the barrel is the same. The question is then asked - which of the two more pure mixtures? The answer is that the mixture will have the same purity.
The problem can be solved by logic and without using computation. No need to declare the volume of wine and water, as long as they are the same. The cup volume is irrelevant, as is mixing stirring.
Video Wine/water mixing problem
Solution
Conservation of substances implies that the volume of wine in a barrel that holds most of the water must equal the volume of water in a barrel that holds most of the wine.
Mixtures can be visualized as being separated into their water and wine components:
To help in understanding this, wine and water can be represented by, say, 100 red and 100 white marbles, respectively. If 25, say, red marbles are mixed with white marbles, and any 25 colored marbles are returned to red containers, then there will be another 100 marbles in each container. If there are now x white marbles in red containers, then there must be x red marbles in white containers. The mixture will therefore have the same purity. The example is shown below.
Maps Wine/water mixing problem
History
This puzzle is mentioned by W. W. Rouse Ball in the third edition, 1896, from his book Recycling Mathematics And Past and Current Problems, and is said to have become Lewis Carroll's favorite problem.
References
Source of the article : Wikipedia
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