Required Mathematical Intelligence

Chapter 123 The Old Lady Sells Live Ducks
An old lady was selling live ducks, and three buyers came, and after a while, they wanted to buy all the ducks.

One of the buyers said: "I will buy half and half of two baskets of ducks." Another buyer said: "I will buy his remaining half and half." The third buyer said: "I will buy what they have left." Half and half."

The old lady thought the three of them were joking, how could they sell half a duck that was alive and kicking.But after thinking about it carefully, he happily sold two baskets of live ducks to them.May I ask: How many live ducks did the old lady sell?How much did each of the three of them buy?
解：先从第三个人入手，买了两人买剩下的一半，还剩一半，而这剩下的一半的对应量是半只，所以，第二个人买了鸭子后还剩0.5÷（1-1/2）=1只。然后再找第二个人买的一半后剩下的量的对应分率，是1 1/2=1.5（只），所以第一个人买后还剩下1.5÷（1-1/2）=3只，最后找第一个人买了一半后的对应量，是3 1/2=3.5只，所以老大娘共有3.5÷（1-1/2）=7只，第一个人买了7/2 0.5=4只，第二个人买了（7-4）÷2 0.5=2只，第三个人买了7-4-2=1只。

[Answer: The old lady sold a total of 7 live ducks, the first person bought 4, the second person bought 2, and the third person bought 1. ]
(End of this chapter)