# A thinking problem (the idea of the application of binary enumeration) cut gold bars

2021-09-15 08:14:17

Today I saw an interesting thinking problem ：

You let a worker work for you for seven days , Pay with a gold bar . Gold bars are divided into 7 A small piece , You can pay a dollar a day .

however , If you can only cut the gold bar twice , So how do you cut gold bars , It can meet the requirement of paying one piece to workers every day ？

It seems to be an ordinary problem , Actually, it's binary , Did you find out ？

That is to say ： The first day is for the workers 1 A small piece , The next day, the workers should be accumulated 2 A small piece , On the third day, it should be accumulated to the workers 3 A small piece .... And so on . That means I cut the gold bar into 3 Share （ Two knives ）, These three can be put together separately 1,2,3,4,5,6,7 Right .

The answer is divided into These three copies ：

The first day ： Give it to him 1                                       1

the second day ： Give it to him 2,3, bring back 1                    2

On the third day ： Give it to him 1　　　　　                1+2

The fourth day ： Take back 1,2,3, Give it to him 4,5,6,7            4

Fifth day ： Give it to him 1　　　　　　　      　1+4

Sixth days ： Take back 1, Give it to him 2,3, 4,5,6,7       2+4

Seventh days ： Give it to him 1　　　　　　　　　1+2+4

It's interesting ？ All non-zero natural numbers in nature , It can be done by 1,2,4,8,16,32,64,128,256,512,1024.......... form

Because all those non-zero natural numbers can be converted into 2 Base number 01 In the form of ,0 Yes, No ,1 Is to take .

There is a similar question ,1000 An apple ,10 A box , this 10 You can decide how many apples there are in each box , As long as the customer reports one at random 1000 Apples within a non-zero number , You can give him some boxes, and the total number of apples in these boxes is the number reported by the customer .

10 Put two boxes separately ：1,2,4,8,16,32,64,128,256,489

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