Intro
Flying from Beijing to Chengdu at night, the airport terminal spent 23 yuan to buy a bag of spicy beef jerky. With no change on his body, he took a 100 to find 77 for the salesman. Suddenly think this thing is too fun. Chinese currency is issued in 100, 50, 20, 10, 5, 1 of these denominations of banknotes. Why should our denominations be designed like this? What if you don't design? Assuming that the design of these denominations is reasonable, then what proportion of these banknotes to be issued in order to ensure that we live in 100 to find 73 of this seemingly simple thing can be normal? The earth is amazing.
Why is the denomination so designed?
What does the denomination design affect us? What is the goal of denomination design? If I arbitrarily design denomination 1,4,5,8,9 this way. It seems unreasonable, but what's wrong with it? We do not want to understand this problem, we do not know how the denomination design is reasonable, but also do not know what to consider when designing the denomination.
If we only issue $100 in banknotes. This means that the currency denomination itself cannot support the trading of goods valued at $100, indicating that the denomination design needs to consider "usability".
If we only consider availability, we can only issue $1 in banknotes. Theoretically, we can buy any amount of goods with N $1. However, if you want to buy something 99 yuan, it began to tragedy. This indicates that the denomination design needs to consider "convenience".
If we think the only consideration for convenience is the number of banknotes we need to pay when we pay. So, why don't we issue a single note for each denomination? For example, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14...97, 98, 99 yuan, so that any amount within 100, we need only one note is enough. I just need to give the salesman a 23 note on the airport.
The question is, how do I know I'm going to the airport and I want to buy that bag of 23 dollars of spicy beef jerky. Instead of the 30 spiced beef jerky next to it? If I do not know in advance, or it is difficult to predict, then I just need to pay a note for the "convenience", I would like to prepare 1~99 denomination notes each, on the body at any time to carry 4950 yuan, altogether 99 banknotes, we can say this is convenient?
Therefore, we need not only consider the availability and the most intuitive convenience in the design of banknotes, but also take into account "the time of the cash transaction, the amount of uncertainty". Because of this uncertainty, which in turn affects our "convenience", we design the editorial denomination not only to pay a certain amount of convenience, but to pay any amount of convenience.
Think again, if use 1,4,5,8,9 this way to design, what question is there? Assuming we have the same probability of 1~9 appearing, we can get the most "convenient" table
1:1 piece of 1 yuan
2:2 piece of 1 yuan
3:3 Piece of 1 yuan
4:1 Piece of 4 yuan
5:1 Piece of 5 yuan
6:1 Tickets 5 Yuan + 1 Zhang 1 yuan
7:1 sheets of 5 Yuan + 2 1 yuan
8:1 Sheets 8 RMB
9:1 Sheets 9 RMB
Statistics: 1 yuan note the probability of appearing is: 5/9, 5 yuan note the probability is: 3/9,4\8\9 appears the probability is: 1/9, this shows that our design itself is not symmetrical. 4\8\9 such a denomination designed to be used by people is very small probability, we do not provide such denominations. "Usage rate".
If you are designing in such a way as 1,2,5:
1:1 piece of 1 yuan
2:1 piece of 2 yuan
3:1 Tickets 1 Yuan + 1 Zhang 2 yuan
4:2 Sheets 2 RMB
5:1 Piece of 5 yuan
6:1 Tickets 5 Yuan + 1 Zhang 1 yuan
7:1 sheets of 5 Yuan + 2 1 yuan
8:1 sheets of 5 Yuan + 1 2 yuan + 1 Zhang 1 yuan
9:1 sheets of 5 Yuan + 2 2 yuan
Statistics: 1 banknotes The probability of appearing is: 5/9, 2 yuan note the probability is: 6/9, 5 yuan banknotes appear probability is: 5/9. Almost like a touch.
We did not involve change in the discussion above. The reason is very simple, for example, I bought 23 yuan of beef jerky, I gave 100. In fact, the problem becomes the salesperson how to give me 77. So the question is constant, how to construct a certain amount with the fewest banknotes, the core of the problem is not who constructs it, if I happen to have a pile of change, it's time for me to break my finger and get some money. Therefore, the focus of our design can be simplified to how to "convenient" construction amount.
The above example is purely fictitious, we do not have RMB 2 yuan denomination. That's the question, why is the denomination design of our renminbi so without the symmetry of beauty? Why do we have 20 yuan denomination, but not 2 yuan denomination? It's a random decision? "50, 20, 10", "5,2,1" not more aesthetic? What does it mean if we don't have a denomination of 2 dollars? The increase in denominations of 1 yuan? Is it because we have 1 dollars of coins? Then why do we have coins again? With banknotes, what is the need for coins to exist?
In what proportion are banknotes issued?
If we were to design according to the current denomination of RMB 1,5,10,20,50, what proportion would we need to distribute the various banknotes?
After answering the question of how to design the denomination, the problem is now easy, and we assume that the probabilities of 1~99 appear the same. Then we just have to list the simplest way of each amount, and then we can count the proportions. Don't want to forget it (count it).
From change to the denomination design of the people's currency
