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 at a time,

Red ball and

Three white balls, so when there are no white balls, there are 50 red balls left. 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 below, ABCD is a parallelogram with an area of

72 square centimeters, e and f are AB and BC respectively.

Point, the area of the shaded part in the figure is _ _ _ _ flat.

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, with the smallest sum.

It 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; Exceeding 10 degrees without exceeding.

20 degrees, 0.80 yuan per degree; For the part exceeding 20 degrees, 1.50 yuan will be charged for each degree. Within one month, user A paid 7. 10 yuan more than user B.

If user B pays 3.75 yuan more than user C, then user A, user B and user C will 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. As we all know, cars are very fast.

The speed of the truck is three times, and the speed of reversing the two cars is their own speed; The distance a car needs to reverse is four times that of a big truck. if

The speed of the car is 50 km/h, so it takes 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. Known participating language groups

52 people, only 16 people in the language group participated; 6 1 person participated in the English group, and only 15 people participated in the English group; There are 63 participants in the math group.

There are 2 1 people who only participate 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. 1 between 2000 and 1 divided by 3,4,5 * * has _ _ _ _.

3. It is known that the multiplication of 1, 1×2×3×N has 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. If today is Saturday, the day after 102000 is _ _ _ _ _.

5. As shown on the right, in the parallelogram ABCD, AB= 16,

AD= 10, BE=4, then FC = _ _ _ _ _ _

6. All natural numbers N suitable for inequality

The total is _ _ _ _ _.

7. There is a clock, which 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 propagates longitudinal waves and shear waves in all directions at the same time. The propagation speed of longitudinal wave is 3.96 km/s, and the propagation speed of shear wave is

2.58 km/s. For an earthquake, the seismic detection point receives the longitudinal wave of the earthquake with a seismograph, and it takes 18.5 seconds to receive the transverse wave of the earthquake.

Wave, then the epicenter of this earthquake is _ _ _ _ _ kilometers away from the earthquake detection point (accurate to one place).

9. A piece of ice loses half its weight every hour. After eight hours, its weight is 5/ 16 kg, so the initial weight of this ice is _ _ _ _ _ _ _ _ kg.

10. In Class 1, Grade 5, 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, including two students in math and two students in English.

Subjects 12, Chinese and English 14, Mathematics and Chinese 10, so there are at least _ _ _ _ _ in Class One, Grade Five.

People.

1 1. There are 2000 lights on, and each light is controlled by a pull switch. Now it is numbered 1, 2, 3, …, 2000, and then it will be numbered 2.

Pull the multiple of the lamp line, then pull the multiple of the lamp line numbered 3, and finally pull the multiple of the lamp line numbered 5, and pull it for three times.

There is a _ _ _ _ _ light on.

12. There are 25 sheets of paper. Write a natural number not exceeding 5 in red pencil on the front of each piece of paper, and write one in blue pencil on the back.

Is a natural number not exceeding 5. The only restriction is that the blue numbers written on any two pieces of paper with the same red numbers cannot be the same. at present

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 were _ _ _ _ _ _ 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. such as

If all are sold at the price of 3 sets of K yuan, you can make 20% investment, and 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 figure on the right, the angle AOB=90o, C is the midpoint of AB arc, and the area of known shadow armor is

16 square centimeter, then the area of shadow b is _ _ _ _ _ square centimeter.

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

9. If stamps with 8 points and 15 points can be taken without restriction, but some postage, such as 7 points and 29 points, cannot be made up, then only 8 points and 15 points will be used.

stamp

The maximum postage that cannot be collected 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). Each cage

Only one bird can fly in. 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. As soon as they met, Party A and Party B set sail.

Equal voyage, after meeting, move on. When A arrived in B and B arrived in A, they all returned to their original routes immediately. When two ships meet for the second time, one ship

Less than b ship 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 divided by four different prime numbers, the remainder is 1. The largest even number satisfying these conditions is

____。

There are two three-digit numbers, and their sum is 999. For example, if you put the larger number to the left of the smaller number and point a decimal point between the two numbers, it will be just right.

It is equal to putting the smaller number to the left of the larger number, and counting a decimal point is six times the number formed between the two numbers, then the difference (big subtraction) between the two numbers is

________。

4. 1000 small cubes with a volume of 1cm are combined into a large cube with a side length of 10cm, and the surface is painted and then divided into several original cubes.

Before coming to the small cubes, at least one side of these small cubes was painted with the number _ _ _ _ _ _.

There are 50 students in a class, among whom 28 take part in Chinese contest, 23 in math contest and 20 in English contest.

Two subjects, then there are at most _ _ _ _ _ people who attend the two subjects.

6. A and B have a 100 meter race. When a reaches the finish line, b is 20 meters behind a; If two people have the same speed, we will make a and b two.

When people reach the finish line at the same time, the starting line of A 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 pumped out in 6 hours.

Drainage; 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, which is a known triangle.

The areas of PAB and triangular PCD are 7 square centimeters and 3 flat, respectively.

Square centimeter, then the area of parallelogram ABCD is _ _ _ _ square centimeter.

9. Party A, Party B and Party C all set out from place A at the same time, ran to places B, C and D respectively, and then ran back immediately, ran back to place A and ran separately.

Go to B, C, D, and then run back to A at once, so keep running back and forth. B is a110km, c is A 1/8km, and d is A 3/ 16km.

Run 3.5 kilometers per hour, B runs 4 kilometers per hour and C runs 5 kilometers per hour. Q: It takes three people to get back to the starting point for the first time.

It will take _ _ _ _ _ hours.

10. A box contains 100 cards, numbered from 1 to 100. Someone randomly selected cards from the box. If at least two cards need to be removed,

The label is 5, so this person needs to draw at least _ _ _ _ _ cards.

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 rectangular ABCD (see the picture below) to point D. After A arrives at point D at 8: 20, C and D will arrive immediately.

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. There is a wooden stick with the length of 1 cm, 2 cm, 3 cm, ... and 9cm (breaking is not allowed according to regulations). Choose several groups.

There are _ _ _ different ways to form a square.

20 10 elementary school mathematics Olympic 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.