1. Reverse thinking: from the result of the problem, reverse thinking about the method to solve the problem. For example, the question is "The square of a number is 8 1. What is this number?" You can think in reverse, first find the square root of 8 1, which is 9, and then think in reverse, find the square root of 9, which is 3.
2. Induction: Find a solution to the problem by observing and summarizing the law. For example, if the question is "the square of a number MINUS this number equals 8, what is this number?" It can be observed that when this number is 4, the condition (4 2-4 = 8) is satisfied, so this number is 4.
3. Recursive method: Through a series of deduction and calculation, the solution of the problem is gradually approached. For example, if the question is "A number plus half of it equals 6, what is this number?" You can set this number to x first, and then get the equation x+0.5x=6 according to the meaning of the question, and solve the equation to get x=4.
4. Graphic solution: turn the problem into a graphic problem, and find a solution to the problem by observing and analyzing the characteristics of the graphic. For example, the question is "The diagonal length of a square is 10. What is the area of this square?" By drawing, we can find that the diagonal of the square divides the square into two isosceles right-angled triangles. According to Pythagorean theorem, the side length of a square is sqrt (102/2) = sqrt (50) = 5 √ 2, so the area of the square is 5√2*5√2=50.
5. Logical reasoning: Through logical reasoning and analysis, find a solution to the problem. For example, if the question is "How much is a number divided by 3 equals 2, divided by 5 equals 3, and divided by 7 equals 2?" Through logical reasoning, it can be concluded that this number minus 2 can be divisible by 3, 5 and 7, that is, this number minus 2 is a common multiple of 3, 5 and 7. Because 3, 5 and 7 are pairwise coprime, their least common multiple is 3*5*7= 105, so this number is 105+2= 107.
The above are some common ideas for solving interesting math problems, and different problems may require different ideas. In the process of solving problems, we can choose the appropriate thinking way according to the characteristics of the topic and our own way of thinking.