One seventh of the first knife and two seventh of the second knife.
This is divided into three sections: one seventh, one half and one quarter.
Then exchange according to the daily workload.
How to divide apples, gold bars and rings?
Example 1: Suppose a box can hold any number of apples. What is the minimum number of boxes we need so that we can bring me any number of apples out of 65,438+0,000 apples?
You let workers work for you for seven days, and the reward is a gold bar. This gold bar is divided into seven connected parts, and you must give them a gold bar at the end of each day. If you were only allowed to break the gold bars twice, how would you pay the workers?
Once upon a time, there was a landlord who didn't want to pay long-term workers, so he thought of a way to distribute it in seven parts. Then he gave him an axe and a set of seven rings. The rings are nested one by one, and the ends are not connected. The landlord asked him to chop only one axe, and then he exchanged the corresponding number of rings for his salary every day, that is, one on the first day and two on the second day. . . Seven on the seventh day. How to cut a ring?
Analyze such problems
First of all, understand
2^0+2^ 1+2^2+。 . . 2^A=〔2^(A+ 1)〕- 1
For example, 0 times 2 times 9 times 2 equals 2 10 minus 1.
Why use the power of 2?
Because in binary,
0 and 1 can form any number.
When solving a problem, think of the total as a fraction to be divided into m and n.
Then 2 n > = m n takes the minimum value.
(It can be used as a formula to solve this kind of operation problem)
Example: 1: m = 10002n > =1000, then n = 10, that is,10 boxes, and the number of apples in each box is 0 times of 2 and1times. . . Nine times.
Example 2: If m = 7 2n > = 7, then n = 3, that is, the gold bar should be divided into three parts:12 4.
Example 3: m = 7 2n > = 7, then n = 3, that is, the ring is divided into three parts:12 4. If you cut on the third ring, it will be divided into three parts: 124, so cut off the third one. Divide a gold bar into 1/7, 2/7 and 4/7. Give him 1/7 on the first day, take back 1/7 on the second day, 1/7 on the third day and 65438+ on the fourth day. ..........