First, the least common multiple of 1 to 8 is 840. Because 840 is their common multiple, the eight numbers obtained by adding 1, 2, 3…8 in turn on the basis of 840 can be divisible by 1 to 8 respectively. So the third one is 843.
2:165438+1October 20th
3000-1764 =1236,1236 ÷ 3 = 412. Suppose there is a person in this group, and later he worked for b days, from11. Where b is less than 28, which completely conforms to the form of dividend = quotient × divisor+remainder, where the remainder is less than divisor, so 4 12÷28= 14+20, so the later manual work lasted for 20 days, from165438+/kloc-.
3: 28 kinds.
When 0 3 is added with 0, 1, 2 and 3 5 respectively, there are four results: 0, 5, 10, 15. 13 to 6 3, with 7×4=28 kinds of * *.
4: 1,7, 13, 19
The sum of any two numbers is a multiple of 2, which means that parity is the same, and the sum of any three numbers is a multiple of 3, which means that the remainder divided by 3 is the same. As it is a positive integer, we take 1, followed by 4,7, 10, 13 and so on. But considering the parity, we take 1, 7, 13, 19.
5:6
This problem is a typical butterfly theorem in decimal olympiad. Because BE: AD = 1: 2, the area ratio BEF:EFD:AFD:ABF= 1:2:4:2 (it is specifically proved that you can use the similar knowledge of junior high school or the hourglass model in decimal Olympic numbers), the area of ABED is 9/2 times that of DEF, that is, 9/2.
6:7
The first encounter * * * walked 1 the whole journey, and the second encounter * * * walked three whole journeys. So the second time is three times as long as the first time, and their respective distances are three times as long as the first time. A When we met for the second time, * * * walked more than 2 kilometers, and walked 3 kilometers for the first time, so the whole journey =3×3-2=7.
Besides, these questions are the basic questions in the Olympic Games, which are not difficult. If you put it in the finals of some competitions 20 years ago, even in the finals of some regional competitions, the difficulty is not enough. At best, it can only be used as a preparatory question. So these questions can hardly be IMO questions now.
I hope my answer will be helpful to your study.
Let's adopt it.