2. A two-digit number is equal to the sum of its one-digit number and the square of its ten-digit number. This two-digit number is _ _ _ _ _.

3. Five consecutive natural numbers, each of which is a composite number, and the minimum sum of these five consecutive natural numbers is _ _ _ _ _ _ _.

There are several red and white balls. If you take out a red ball and a white ball at a time, there will be 50 white balls when you can't get the red ball; If you take one red ball and three white balls at a time, there will be 50 red balls left when there are no white balls. Then this pile has _ _ _ _ _ _ _ red balls and white balls.

5. The age of a young man this year (2000) is exactly equal to the sum of the figures of the year of birth, so the age of this young man this year is _ _ _ _ _ _ _.

6. As shown in the right figure, ABCD is a parallelogram with an area of 72 square centimeters, and E and F are the midpoint of AB and BC respectively, so the area of the shaded part in the figure is _ _ _ _ square centimeters.

7.a is a 2000-bit integer composed of 2000 9s, and B is a 2000-bit integer composed of 2000 8s, so the sum of the digits of a×b is _ _ _ _ _ _ _.

8. Four consecutive natural numbers, from small to large, are multiples of 3, multiples of 5, multiples of 7 and multiples of 9, and the minimum sum of these four consecutive natural numbers is _ _ _ _.

9. The charging standard for electricity consumption in a residential area is: the monthly electricity consumption of each household does not exceed 10 kWh, and the charge per kWh is 0.45 yuan; The part exceeding 10 degree but not exceeding 20 degree will be charged 0.80 yuan per degree; For the part exceeding 20 degrees, 1.50 yuan will be charged for each degree. In a certain month, user A pays 7. 10 yuan more than user B, and user B pays 3.75 yuan more than user C, so users A, B and C * * pay _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

10. A car and a big truck met on a 9-kilometer-long narrow road, and they had to reverse the car to continue. It is known that the speed of a car is three times that of a big truck, and the speed of reversing two cars is their own speed; The distance a car needs to reverse is four times that of a big truck. If the speed is 50 km/h, it will take at least _ _ _ _ _ hours to cross this narrow road.

1 1. Grade five students in a school 1 10, take part in Chinese, math and English activity groups, and each student should take part in at least one group. 52 people are known to participate in the language group, and 16 people only participate in the language group; 6 1 person participated in the English group, and only 15 people participated in the English group; There are 63 people in the math group, and only 2 1 person in the math group. Then there are _ _ _ _ _ people in all three groups.

12. There are eight steps, and Xiao Ming goes from bottom to top. If he can only take one or two steps at a time, he may go up in _ _ _ _ different ways.

Preparatory work (b)

1. Calculation: = _ _ _ _ _.

2.2. 1 between 2000 and 1 divided by 3,4,5 * * has _ _ _ _.

3.3. It is known that 1,1× 2× 3××× n is multiplied by n consecutive natural numbers, and there are exactly 25 consecutive 0s at the end of the product, so the maximum value of n is _ _ _ _.

4.4. If today is Saturday, the day after 102000 days from today is _ _ _ _ _ _ _.

5. As shown in the right figure, in the parallelogram ABCD, AB= 16, AD= 10, BE=4, then FC = _ _ _ _ _ _

6. The sum of all natural numbers n suitable for inequality is _ _ _ _ _ _ _ _.

7. One clock is 2 minutes slow every hour. At 8: 00 a.m., aim at the standard time. When the clock arrives at noon 12, the standard time is _ _ _ _.

8. During an earthquake, the earthquake center emits longitudinal waves and shear waves in all directions at the same time, with the propagation speed of longitudinal waves and shear waves of 3.96 km/s and 2.58 km/s. In an earthquake, it takes 18.5 seconds for the seismic detection point to receive the longitudinal waves of the earthquake, so the epicenter of this earthquake is _ _ _ _.

9. A piece of ice loses half its weight every hour. After eight hours, its weight is kilograms, so the initial weight of this piece of ice is _ _ _ _ _ _ _ kilograms.

10. In Class One, Grade Five, 32 students took part in the math contest, 27 students took part in the English contest and 22 students took part in the Chinese contest. Among them, 12 students take math and English, 14 students take Chinese and English, and 10 students take math and Chinese. So there is at least _ _ in Class One, Grade Five.

1 1. There are 2000 lights on, and each light is controlled by a pull switch. Now their numbers are 1, 2, 3, ..., 2000 in turn, then pull the light line with the number of 2, then the light line with the number of 3, and finally the light line with the number of 5. After pulling for three times, there are _ _ _ _ _ _ _ lights on.

12. There are 25 sheets of paper. On the front of each piece of paper, write a natural number of no more than 5 with a red pencil, and write a natural number of no more than 5 with a blue pencil on the back. The only restriction is that the blue numbers written on any two pieces of paper with the same red numbers cannot be the same. Now multiply the red and blue integers on each piece of paper, and the sum of these 25 products is _ _ _ _ _ _ _ _.

The last volume

1. Calculation: = _ _ _ _ _.

2. There are 325 boys and girls, and the number of boys in the new school year has increased by 25; The number of girls decreased by 5% and the total number increased by 16, so there are _ _ _ _ _ _ _ boys.

3. A store bought a batch of tapes at the price of every three sets 16 yuan, and bought twice as many tapes from other places at the price of every four sets1yuan. If all three sets of K are sold at a price of 20%, then the value of K is _ _ _ _ _ _ _.

4. When13511,13903 and 14589 are divided, the largest integer that can leave the same remainder is _ _ _ _ _.

5. Try to express 20 as the sum of some complex numbers, and the maximum product of these complex numbers is _ _ _ _ _ _ _.

6. In the product of 1× 2× 3× ... 100, the 25th number on the right is _ _.

7. As shown in the right figure, the angle AOB=90o, and c is the midpoint of AB arc. Given that the area of shadow A is 16 cm2, the area of shadow B is _ _ _ _ _ cm2.

8. The sum of the digits on each number is 15, and there are _ _ _ _ _ _ * three numbers.

9. If stamps with a score of 8 and 15 can be taken without restriction, but some postage, such as 7 and 29, can't be paid, then the maximum postage that can't be paid for stamps with a score of 8 and 15 is _ _ _ _.

The last two digits of 10. It is _ _ _ _ _.

1 1.4 Birds fly into four different cages. Every bird has its own cage (different birds have different cages), and only one bird can fly into each cage. If you don't fly into your cage, there are _ _ _ _ different ways to fly.

12. Two ships, A and B, sailed in opposite directions at the same time, with A sailing downstream and B sailing against the current. When they met, two ships, A and B, made the same voyage. After they met, they moved on. After A arrived in B and B, they immediately went back the same way. When the two ships met for the second time, ship A traveled less than ship B 1 km. If the time interval from the first meeting to the second meeting is 1 hour for 20 minutes, the flow rate of the river is _ _ _ _ kilometers per hour.

Final (b) volume

1. Calculation: = _ _ _ _ _.

2. Thousands are four digits of 1. When it is divisible by four different prime numbers, the remainder is 1, and the largest even number satisfying these conditions is _ _ _ _.

There are two three-digit numbers, and their sum is 999. If you put the larger number to the left of the smaller number and point a decimal point between the two numbers, it is exactly equal to putting the smaller number to the left of the larger number and point a decimal point between the two numbers, which is 6 times of the number, then the difference (big reduction) between the two numbers is _ _ _ _ _ _ _ _ _.

4. One thousand small cubes with a volume of 1 cm3 are combined into a large cube with a side length of10cm, and the surface is painted and then divided into the original small cubes. At least one side of these cubes has been painted, and the number is _ _ _ _ _ _.

There are 50 students in a class, 28 take part in the Chinese competition, 23 take part in the math competition and 20 take part in the English competition. Each student takes part in at most two courses, so the maximum number of people taking part in two courses is _ _ _ _ _.

6. A and B have a 100 meter race. When a reaches the finish line, b is 20 meters behind a; If their respective speeds remain the same, in order for Party A and Party B to reach the finish line at the same time, Party A's starting line should be _ _ _ _ _ meters behind the original starting line.

7. A pool has a water inlet pipe that keeps feeding water, and several identical pumping pipes. If 24 pumping pipes are used to pump water, the water in the pool can be drained in 6 hours; If you use 2 1 pumping pipe to pump water, you can drain the water in the pool in 8 hours. If 16 pumping pipe is used to pump water, the water in the pool can be drained within _ _ _ _ hours.

8. As shown on the right, p is a point outside the parallelogram ABCD. Given that the areas of triangle PAB and triangle PCD are 7 square centimeters and 3 square centimeters respectively, the area of parallelogram ABCD is _ _ _ _ _ square centimeters.

9. Party A, Party B and Party C all set out from Party A at the same time, ran to Party B, Party C and Party D respectively, then ran back immediately, ran back to Party A, then ran back to Party B, Party C and Party D respectively, and then ran back to Party A immediately, and so on. B is kilometers away from A, C is kilometers away from A, D is kilometers away from A, A runs 3.5 kilometers per hour, B runs 4 kilometers per hour, and C runs 5 kilometers per hour. Q: It takes _ _ _ _ hours for three people to return to the starting point at the same time for the first time.

10. A box contains 100 cards numbered from 1 to 100. Someone randomly draws cards from the box. If the difference between at least two cards required to be drawn is 5, then this person needs to draw at least _ _ _ _ _.

1 1.8 o'clock 10, there are two people, A and B, who are 60 meters apart clockwise at the same speed.

Go along the edge of the rectangle ABCD (see the right) to point D. After A arrives at point D at 8: 20, C and D will be right away.

Starting from point D at the same speed, C goes from D to A, meets B at point E at 8: 24, and D goes from D to C.

Go, 8: 30, and be overtaken by B at point F, then the area of connecting triangle BEF is _ _ _ _ _ square meters.

12. At present, there is a type with the length of 1 cm, 2 cm, 3 cm, ... and 9cm respectively (it is not allowed to break according to the regulations). There are _ _ _ different ways to form a square with several sticks.

Reference answer

Preliminaries A 1, 5 15 1 2, 89 3, 130 4, 250 5, 19 6, 48 7, 18000 8, 642 9, 220.

Preliminaries B 1, 0.5 2, 34 3, 109 4, Monday 5, 8 6, 104 7, 12 8, 29 minutes 8, 137 9, 80/kloc-0.

Finals A 1 2 and 8 5 2, 170 3,194,985,10246,47,168,699,9710.

Finals B 1, 100 2, 1996 3, 7 15 4, 488 5, 35 6, 25 7, 18 8, 8 9, 6 10, 0.