International Mathematical Olympiad, referred to as IMO, is an international competition with mathematics as its content and middle school students as its object. It has a history of more than 30 years.
As an international competition, the International Mathematical Olympiad was put forward by international mathematical education experts, which exceeded the level of compulsory education in various countries and was much more difficult than the college entrance examination. In 20 12 years, IMO has become the most influential academic competition in the world, and it is also recognized as the highest level mathematics competition for middle school students.
The math contest in China started at 1956. At the initiative of famous mathematicians such as China and the Soviet Union, initiated by chinese mathematical society, the four cities of Beijing, Tianjin, Shanghai and Han took the lead in holding high school mathematics competitions.
Olympic issues
1, there are more than 5,000 toothpicks, which are divided into small packets according to the following six specifications: if 10 toothpicks are packed, there are 9 toothpicks left at last; If there are 9 in a pack, there are 8 left in the end; If 8, 7, 6 and 5 roots are packed in turn, 7, 6, 5 and 4 roots are left. How many toothpicks does a * * * have?
Analysis: If you add 1 toothpick, then when you divide it into small packets according to six specifications, each packet is just full and there is no surplus. That is, the number of toothpicks at this time is the common multiple of 5, 6, 7, 8, 9, 10.
The least common multiple of 5, 6 and 7. 8,9 and 10 are 23x3*x5x7=2520, and the original number of toothpicks is more than 5000, so there are toothpicks 2x2520- 1=5039 (root).
2. Choose six prime numbers within 20, and then write these six numbers on six faces of a cube to make the sum of the numbers of two opposite faces equal. Such three building blocks are thrown on the ground. How many different values can the sum of three upward numbers have?
Prime numbers less than 20 are 2,3,5,7, 1 1, 13, 17, 19, where 5+19 = 7+19.
The minimum sum of the three numbers is 5+5+5= 15, and the maximum sum is19+19 = 57. Through experiments, the sum of three numbers can be all odd numbers from 15 to 57, and there are 22 possible different values * *.
Extended data
China's mathematical attributes.
Mathematics competition is a mass extracurricular activity, belonging to folk activities rather than government education projects.
China's Three Principles
First, with the help of the people's society, sponsored by the Mathematical Association, supported by the administrative department, and funded by the education administrative department and the Association for Science and Technology.
Second, streamlining and saving, taking 1979 national mathematics competition as a lesson and giving priority to spiritual rewards.
Third, voluntary participation, students participate in the competition completely by interest, without coercion.