#### Riddle.

23.- We have a container with 10 liters of water and one with 10 liters of wine, three liters of water are poured into the carafe of wine and mixed , then they returned to take three liters of the mixture into the jug of water.

What will be after the change, more water in the bottle of wine or more wine in the bottle of water?

#### Solution

There are two ways to solve this riddle, for half of arithmetic or logic

##### arithmetic option .

By taking three liters of water into wine in the bottle will have 13 liters of wine mixture of those parts will be 3/13 10/13 parts water and wine.

When returning three liters of mixture to the jug of water will have returned 3 * 10/13 liters of wine into the water, or what is the same 30/13 liters of wine in the bottle of water.

When we had 13 liters of mixture into the bottle of wine 3 liters of water were and we said we had 3/13 10/13 parts water and wine parties , to return 3 liters water carafe refund 3 * 3/13 liters of water , or what is the same thing we get 9/13 liters of wine to the bottle , thus stay 3 - 9/13 liters of water in wine , which is equal to 39 / 13-9 / 13 which it is equal to 30/13 liters of water in the wine.

Therefore the arithmetic mean we know that we have the bottle of wine 30/13 liters of water and the water 30/13 liters of wine .

##### logical choice.

After making the mixture into two bottles continue to have 10 liters , so the water that we lack a bottle has been replaced by the same quantity of wine and vice versa in the other bottle , the two bottles have the same amount liquid from the other which is what we asked the problem.

The latter solution is faster , we know the answer to the riddle is that the two bottles are the same part of the other, but we do not know what the amount, the arithmetic mean if we knew .