1 There are 4 piles of balls with the same appearance, with 4 balls in each pile. It is known that three piles are genuine and one pile is defective. Each quality ball weighs 10g, and each quality ball weighs11g.. Please weigh it with a balance and find out the defective pile.

There are 27 balls with the same appearance, and only one ball is defective, which is lighter than the genuine one. Please weigh it with the balance only three times (no weight) to find out the defective ball.

3. According to 10 balls with the same appearance, only one ball is defective. Please weigh it three times with the balance to find out the defective products.

There are 12 balls with the same appearance, and only one ball is defective. Only use the balance to weigh it three times. Can you find out the defective products?

Olympic Special Topic-Pigeon Cage Principle

1. A certain group * * * has 13 classmates, at least two of whom have birthdays in the same month. Why?

2. Any four natural numbers, in which the difference between at least two numbers is a multiple of 3. Why is this?

3. There are 15 socks of the same color and size mixed in the box. How many socks can you take out of the box at least to ensure three pairs of socks (socks are left and right)?

Olympic theme-restoration problem

1. Someone went to the bank to withdraw money. The first time, he took more than half of the savings in 50 yuan, and the second time, he took more than half of the remaining 100 yuan. At this point, there is 1250 yuan left in his passbook. What was his initial deposit?

There are 26 bricks, and the two brothers are scrambling to pick them. The younger brother is in front of them. Just after laying bricks, my brother came. My brother saw that my brother picked too much, so he took half of it himself. The younger brother thought he could do it, so he took half from him. My brother wouldn't let me, so he had to give him 5 pieces, so my brother picked 2 pieces more than his brother. How many pieces was my brother going to choose at first?

Olympic theme-train crossing the bridge

1. A 300-meter-long train crosses the bridge at a speed of 1080 meters per minute. It takes 3 minutes to get off the bridge from the front to the rear. How long is this bridge?

2. Someone walks at a speed of 2 meters per second. A train came behind, which took 10 seconds longer than him. As we all know, this train is 90 meters long. Find the speed of the train.

3. On the circular track, when two people run clockwise, they meet every 12 minutes. If the speed of two people is the same, one of them will run counterclockwise and meet every 4 minutes. How many minutes does it take each person to run a lap?

4. A 300-meter-long train passes through a 940-meter-long bridge at a speed of 1080 meters per minute. How many minutes does it take to get off the bridge from the front to the rear?

It takes 40 seconds for a train to cross a 530m bridge and 30 seconds for a 380m cave at the same speed. What is the speed/second and total length of this train?

6. The distance between telephone poles along the railway is 40 meters. When a passenger is in a running train, it is exactly 2 minutes from seeing the first pole to seeing the fifth/kloc-0 pole. How many kilometers does the train travel per hour?

7. A man was standing by the railway. After hearing the whistle of the nearest train, the train passed in front of him in 57 seconds. It is known that the train whistle is1360m away from him; The speed of sound is 340 meters per second. What is the speed of the train? (Numbers are reserved as integers)

How many seconds does it take for a 450-meter-long truck to cross a 570-meter-long iron bridge at a speed of 12 meters per second?

8. At present, two trains run in the same direction at the same time. /kloc-After 0/2 seconds, the express train will overtake the local train. The express train runs18m per second, and the local train runs10m per second. If two trains travel in the same direction at the same time, the express train will overtake the local train in 9 seconds, and find the body length of the two trains.

9. Li Minghe Zhang Yi practiced running on the 300-meter circular track. Li Ming runs 5 meters per second, and Zhang Yiran runs 3 meters per second. Both of them started from the starting point and went in the same direction. How many meters did Zhang Yi run when Li Ming caught up with Zhang Yi for the first time after departure?

The speed of three cars is 10. The fast, medium and slow cars start from the same place at the same time and catch up with the cyclist in front along the same highway. The three cars caught up with the cyclist in 6 minutes, 10 minutes and 12 minutes respectively. Now we know that the express train is 24 kilometers per hour and the bus is 20 kilometers per hour, so how many kilometers per hour is the local train? (choose to do the problem)

1 1 On the circular runway with a circumference of 400 meters, there are two points, A and B, which are 100 meters apart. A and b run away from each other at the same time. After they met, B immediately turned and ran in the same direction as A. When A ran to A, B just ran to B. If A and B ran at the same speed,

Olympic theme-average problem

Final exam 1, Cai Chen scored 89 points in political language, mathematics, English biology, 9 points in political mathematics, 84 points in Chinese English, 86 points in political English, and English was more than Chinese 10.

The fruit shop mixes 2 kilograms of crisp candy, 3 kilograms of fruit candy and 5 kilograms of milk candy into assorted candy. Known crisp candy is 4.40 yuan per kilogram, fruit candy is 4.20 yuan per kilogram, and milk candy is 7.20 yuan per kilogram. Q: How much is the assorted candy per kilogram?

There are two cotton fields, A and B, with an average yield per mu1.85kg.. A has 5 mu of cotton fields, with an average yield of 203 kg per mu. B Average yield per mu of seed cotton in cotton field170kg. B How many acres of cotton fields are there?

It is known that the sum of eight consecutive odd numbers is 144. Find these eight consecutive odd numbers.