The problem is: a peasant woman went to the market to sell eggs, and sold half of all the eggs for the first time; The second time, I sold half of the remaining eggs; The third sale was half of the remaining eggs sold in the previous two times, and the last sale was half of the remaining eggs. The eggs are just sold out at this time. I asked the peasant woman how many eggs she had.

Many mathematicians are interested in this problem and have given many solutions, but most of them are complicated. Euler, a famous Swiss mathematician, gave a unique solution to this problem: let the remaining eggs after the third sale (the fourth sale) be 1+0.5, the eggs sold for the third time be (1+0.5) times 2 = 3, and the number of eggs left after the second sale should be: (3+0.5) times 2 =.

We are inspired by Euler's thinking on the above problems: some mathematical problems are sometimes difficult to start with or can't be solved at all, but if we can think reversely according to the conditions provided by the problems, there is hope to be solved. Euler's solution to the problem of peasant women selling eggs is the concrete embodiment of this reverse thinking mode.