First, use ① ~ ⑨ to mark five spaces from left to right. Of course, if the equation is solved and the sum of each circle is equal to 13 or 14, then there are six permutations when the nine numbers 1 to 9 are filled into the circle.

permutation and combination

Permutation and combination is the most basic concept of combinatorics. The so-called arrangement refers to taking out a specified number of elements from a given number of elements for sorting. Combination refers to taking out only a specified number of elements from a given number of elements, regardless of sorting.

The central problem of permutation and combination is to study the total number of possible situations in a given permutation and combination. Permutation and combination are closely related to classical probability theory.

Development history

Although mathematics began in ancient times, there was no skill because the development of social production level was still in the low stage.

With people's understanding and research on numbers, in the process of forming mathematical branches closely related to numbers, such as the formation and development of number theory, algebra, function theory and even functional, the diversity of numbers is gradually discovered from the diversity of numbers, and various counting skills are produced.

At the same time, people have a profound understanding and research on numbers. In the process of the formation and development of various mathematical branches closely related to shapes, such as geometry, topology and category theory, the diversity of numbers and shapes is gradually discovered from the diversity of shapes, and various skills of numbers and shapes are produced.

Modern set theory and mathematical logic reflect the potential combination of number and shape. However, modern algebraic topology and algebraic geometry closely link numbers with shapes. All these have had and will continue to have a far-reaching impact on the formation and development of modern combinatorics centered on digital skills.

From this point of view, combinatorics is closely related to other branches of mathematics. Some of its research contents and methods come from various branches and are also applied to various branches. Of course, combinatorics, like other branches of mathematics, has its own unique research problems and methods, which stem from people's discovery and understanding of numbers, shapes and their relationships in the objective world.

For example, in the Book of Changes in ancient China, the period of 60 years was recorded by ten heavenly stems and twelve earthly branches, and the Rubik's Cube was recorded in the river map of Luoshu, which was the earliest combination problem and even architectural contextualism.