水与酒
Water & Wine
题目详情
有两只等容量杯子：杯 A 装满水，杯 B 装满酒。
从杯 A 舀一勺倒入杯 B 混匀；再从杯 B 舀一勺（同样体积）倒回杯 A。
问：杯 A 中混入的酒的量，是否等于杯 B 中混入的水的量？
There are two jars, one contains water, and the other contains wine (equal volumes). A certain amount of water is transferred to the wine, then the same amount of the mixture is transferred back to the water beaker. Is there now more water in the wine than there is wine in the water?
Assume there is no expansion, compression, spillage or any chemical reaction.
Hint
If the two jars contain the same volume of liquids initially and finally, then why would be one more impure?
解析
相等。
因为两杯最终体积仍各自保持不变。杯 A 里“酒的增加量”必然等于杯 A 里“水的减少量”；而杯 B 里“水的增加量”正好等于杯 A 里“水的减少量”。因此杯 A 混入的酒量 = 杯 B 混入的水量。
Original Explanation
Equal!
Solution
The final volumes of both the mixture-liquids are equal. This means in the first jars, the combined volume of water & wine is the same as that of jar B. Assume that the original volume is . Suppose the final volume in the first jar is for water and for wine. This implies that the second jar has amount of wine and of water. This proves that there are equal amounts of water in the wine jar and wine in the water jar.