1. Title: Add 7 and subtract 5 from a certain number, and the result is 12. Find this number. Answer: 14

Analysis: According to the description of the topic, we can list the following formulas: (x+7-5)= 12, and the solution is x= 14.

2. Title: There are two three-digit numbers added together, and the sum obtained is the first number of a four-digit number. What are these two three digits? Answer: 457 and 542.

Analysis: According to the description of the topic, we can list the following formulas: the sum of two three digits is 1000-999= 10000, because their sum is a four-digit prefix, so the sum of these two three digits can only be 1000. So these two three digits are 457 and 542 respectively.

3. Title: There is a number whose single digit is 2 larger than the ten digits. This number is more than 70 and less than 90. What's this number? Answer: 73.

Analysis: According to the description of the topic, we can list the following equations: the number of units is 2 larger than the decimal number, so this number can be expressed as 10x+y, where X is a decimal number and Y is a singular number, and since this number is more than 70 and less than 90, we can list the following inequalities: 70.

4. Title: There is a square and a rectangle, and their perimeters are equal. It is known that the side length of a square is 4 cm and the length of a rectangle is 10 cm. Find the width of the rectangle. Answer: 6 cm.

Analysis: According to the description of the topic, we can list the following equations: the circumference of a square is 4x4= 16 (cm), and the circumference of a rectangle is 2 (length+width) = 16 (cm). Given the length of 10 cm, the width can be (16-2x 10)/2=3 (cm).

5. Title: There is a box with red balls and black balls in it. It is known that the number of red balls is twice that of black balls, and the number of red balls is two more than black balls. How many red balls are there in this box? Answer: 8.

Analysis: According to the description of the topic, we can list the following equations: the number of red balls is twice that of black balls, which can be expressed as red balls =2x, black balls = x, and Chang Min can get that the number of red balls is x+2, because the number of red balls is two more than black balls. Combining the above two equations can get X=2, so the number of red balls is 8.

Characteristics of Olympic mathematical thinking;

1, high difficulty: Olympic math problems are usually more difficult than school math problems, and students need to use more advanced thinking and methods to solve them.

2. Multi-level: The topic of Olympic Mathematics is from primary school to high school, which is suitable for students of different ages and different mathematical levels, so that students' mathematical ability can be gradually improved.

3. Cultivate comprehensive ability: Olympic Mathematics focuses on cultivating students' logical thinking, problem-solving ability and creativity, not just memorizing and taking exams.

4. International communication: The Olympic Mathematics Competition is very popular in the world. Students can meet math lovers from all over the world by participating in international math competitions, which is conducive to broadening their horizons.

5. The combination of divergent thinking and convergent thinking: The Olympic math problem requires students to find a balance between divergent thinking and convergent thinking, think about the problem from multiple angles, and then sum up the correct answer.