A question about the principle of drawer There are five arbitrary points in the rectangle with 6cm and 8cm sides (including the boundary). The distance between at least two of the five points is less than 5cm. Why?

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• 1. 1. From 1 to 36, how many numbers can be taken at most so that the difference between the two numbers is a multiple of 5? 2.1 to 100, take at least several numbers to ensure that one of them must be divisible by 5?
• 2. The topic of drawer principle 1. Proof: in any five integers, three numbers must be taken out, so that their sum can be divided by three 2. A school sent 204 students to plant 15301 trees on the mountain, among which at least one person planted 50 trees and at most one person planted 100 trees, proving that trees planted by at least five people were the same
• 3. On the principle of drawer Among the six monkeys on monkey mountain, one must have got at least five peaches. How many peaches are there in this pile?
• 4. If x and y are inversely proportional and y = 12 when x = 16, then when x = 10, y = ()
• 5. This is our teacher Li
• 6. New year's greetings to teachers of mathematics, Chinese, English, physics, chemistry, biology, politics and geography. Thank you!
• 7. New year's day, English teachers each send a new year's message Especially the math teacher's must be good. All the homework will be sent to us at the first time (all new, not so conventional)
• 8. Answer the following three practical questions (the third one is based on proportional knowledge) 1. Hongxing primary school bought 135 meters of plastic rope skipping, and the swordsman made five rope skipping from 9 meters. According to this calculation, how many pieces of plastic rope can be made with the rest? 2. Dilute 400g of 8% sugar water with water to 5% sugar water. How many grams of water should be added? 3. A and B cars leave from two places 360 kilometers apart at the same time, and they run in opposite directions. They meet four hours later. The speed ratio of a and B cars is 2:3. How many kilometers per hour do a and B cars walk?
• 9. Percentage application questions knowledge points! For example: how many percent of one number is another
• 10. There is a practical problem. I will, An elephant weighs 2.6 tons, 0.25 tons less than three times the weight of a cow,
• 11. A drawer principle problem, but also analysis The summer camp organizes activities for 200 students, including visiting famous schools, surfing on the sea and mountain climbing. It is stipulated that each student must participate in one or two activities, so how many students participate in the same activities at least?
• 12. How to do the problem of cutting off the remaining volume of a small cone in a cone The poem goes like this: on a cone with a bottom radius of 6 decimeters, cut off a cone with a bottom radius of 3 decimeters. The known cut off part is the volume of 27 cubic decimeters
• 13. Super difficult exercises of solving cylinder and cone More is better! Thank you very much!
• 14. Exercises of cylinder and cone 1. The bottom surface of a cylinder is divided into several sectors, and then cut into an approximate cuboid. The surface area of the cuboid is increased by 200 square centimeters. Given that the height of the cylinder is 20 cm, the volume of the cylinder is calculated 2. In a cylindrical glass container with a bottom radius of 10 cm and a water depth of 8 cm, a piece of iron with a length of 8 cm and a width of 15 cm and a height of 10 cm should be put into the container ① If you put the iron in the water, how many centimeters will the water rise? ② If you put the iron in the water, how many centimeters will the water rise?
• 15. There are two equal bottomed cylinders. The height of the first cylinder is 45 times that of the second cylinder. The volume of the first cylinder is 3.2 cubic centimeters. How many cubic centimeters more is the second cylinder than the first one?
• 16. Fill in the blanks: 1. The radius ratio of a cylinder to a cone is 2:3, the height ratio is 3:2, and the volume ratio is（ 2. If the bottom radius of the cone is constant and the height is increased by 2 times, the volume is () times of the original. If the height of the cone is constant and the bottom radius is increased by 2 times, the volume is () times of the original 3. There is a piece of iron sheet, which can be used for 8 sides of cylindrical oil drums or 24 bottoms of cylindrical oil drums of uniform specifications. Ten pieces of iron sheet can be used for () such oil drums No need to write process
• 17. There are 32 bottles of 100kg oil. How many large and small oil bottles are there?
• 18. There are 50 chickens and 160 feet in the same cage. If all chickens are assumed to be rabbits, then 50 rabbits will have (?) feet, which will be more than the actual (?): Why are there so many more chickens? Because if a chicken is assumed to be a rabbit, it will have (?) feet, which will be more than the actual (?) = (?), we need to divide (?) by (?) = (?) if a chicken is assumed to be a rabbit, then rabbits will have (?) - (?) = (?)
• 19. Put 7 pieces of iron into 3 boxes, at least 3 pieces of iron sheet should be put into the same box. Why?
• 20. A+A+A+A+A=100 (B + b) / (division sign) a = 100 B+A+B+A-C=100 Then: a = () B = () C = ()