1, digital reasoning: observe the relationship between existing numbers and try to find out the law. According to these laws, the number to be filled in is inferred. Series: If the box is a series, you can try to find patterns or laws between numbers in the series. For example, you can check whether there are arithmetic progression, geometric series and Fibonacci series.

2. Numeric operation: Sometimes, the number given in the box may be the result of some mathematical operation. You can try to use operations such as addition, subtraction, multiplication and division to infer the number to be filled in according to the existing numbers.

3. Graphic shape or arrangement: If the box is a graphic or arranged fill-in-the-blank question, you can observe the rule of graphic shape, position or pattern and the relationship between numbers. Reasoning according to these rules and filling in the appropriate numbers. Logical reasoning: use logical reasoning and common sense to infer the possibility of filling in numbers according to the existing information and the conditions of the question.

4. Characteristics and attributes of numbers: Observe the characteristics and attributes of numbers in the box, such as the parity of numbers, the relationship between prime numbers and non-prime numbers, the square or cube of numbers, etc. According to these characteristics, try to fill in the figures that conform to the law.

5. Sum or product of numbers: If the sum or product relationship between numbers is given in the box, the filled numbers can be calculated according to the sum or product of existing numbers. Location of vacancy number: observe the location of vacancy number and surrounding numbers, and try to find out the relationship between numbers. This may involve rows, columns, diagonals or other specific positional relationships.

Boxes have many applications in mathematics.

1. Fill in the blanks with numbers: boxes are usually used to fill in the blanks with numbers, and appropriate numbers need to be filled in according to given rules or relationships. This kind of topic is helpful to cultivate mathematical logical thinking ability and reasoning ability. Math problems: Math problems can be done in boxes. This is helpful to practice mathematical operations and solve practical problems.

2. Sequence problem: The sequence problem often uses a box, in which a series of numbers are given, and it is required to guess the missing number or fill in the next number. This is helpful to cultivate the ability to observe the relationship between numbers and discover laws.

3. Geometric problems: boxes can be used in geometric problems, such as filling in missing side length, angle or graphic attributes. This is helpful to practice the ability of geometric reasoning and graphic analysis.