1, arrange the number of 10 in a line from 1 to 10, so that the sum of every three adjacent numbers is a multiple of 3, and * * has XX arrangement methods.

2. Take out two small squares with common vertices but no common edges from a 3×3 square. A * * *, how many different ways can there be?

Xiao Gang and Xiao Yong ran 50 meters. When Xiao Gang reached the finish line, Xiao Yong was still behind Xiao Gang 10 meter. In the second race, Xiaogang's starting line retreated 10 meter, and the two men still ran at the first speed, so whoever reached the finish line first, at this time, the other side was XX meters behind.

4. Two cars, A and B, drive from directions A and B at the same time, passing a gas station at 9 am and afternoon 1 respectively. As we all know, A is three times as fast as B ... and then two cars meet at point X.

The essence of the Olympics:

The Olympic Mathematics is relatively in-depth, and the vigorous development of mathematical olympiad has greatly stimulated children's interest in learning mathematics, which has become a useful activity to guide them to be positive, explore actively and grow healthily. There are many practical problems, such as counting, graph theory, logic, pigeon hole principle and so on. To solve this kind of problem, it is generally necessary to analyze and summarize the mathematical significance of the actual problem, abstract the actual problem into a mathematical problem, and then use the corresponding mathematical knowledge and methods to solve it.