Most of the seats on the hard seats of the train, the bullet train and the high-speed rail are arranged with a 3+2 number of seats, and the aisle is in the middle. Why is it designed this way?
Some might say: to carry more passengers, of course. In fact, in addition to factors such as ride comfort and space accommodation, the reason for this design is also mathematical considerations.
So, what are the benefits of this arrangement?
Imagine traveling on the high-speed train with your family and friends, and everyone wants to be seated next to each other and don't want to be separated from their companions.
At this time, if the number of people traveling is 2 people, you can choose 2 seats, 3 people can choose 3 seats, if the number of people is more than 4 people, you can choose 2 rows of 2 seats, and if there are 5 people, you can choose 2 seats and 3 seats in each row, so that you can just sit down and not separate from each other.
That's right, the 3+2 seat design is designed to allow groups of passengers to sit next to each other without being separated.
Some people may ask, can we ensure that everyone is seated together when there are more people?
We can put this question another way: "Can all integers above 2 be obtained by adding the numbers 2 and 3 appropriately?"
When the total number of people is even, it is not difficult to see that dividing by 2 (2-seater) is just enough to allocate. If it is an odd number, you can also choose a row of 3 seats, and divide the remaining number of people by 2 (2 seats).
In other words, as long as there are 2 and 3 people in the seat, no matter how many people (more than 2 people) there are in a group, the group members can sit next to each other, and no one will be left alone or shared with strangers.
The high-speed rail seat problem is based on the Frobenius Coin Problem. The original question was: "Given a few denominations, what is the maximum amount that cannot be paid with these coins?"
This problem was named after the German mathematician F. G. Frobenius (1849~1917).
Frobenius, German mathematician
图片来源：Wikipedia
For example, if there are only $3 and $5 coins, then the maximum amount that cannot be paid is $7 (in the figure below, for illustrative purposes, let's assume that there are $3 and $5 coins).
The key point of the high-speed rail seat and the Frobenius coin problem is to see whether the numbers are prime numbers with each other, such as 2 and 3, 3 and 5, etc. If two or more integers have a common factor of only 1, then the two or more numbers are coprime. When two numbers are coprime, they can make up any number that is greater than a certain value.
In the Frobenius coin problem, suppose there are two denominations, A and B, and A and B are mutually primitive, and the maximum amount that cannot be paid with these two coins is:
A×B-A-B=(A-1)(B-1)-1
Substituting the specific numbers (A=3, B=5) to calculate, the answer is 7. Therefore, $3 and $5 coins can pay any amount of $8 and above.
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Has strange knowledge increased again?
Source: Science World
Editor: Apo