Find 30 Olympic math problems in grade one.

1. It is known that the equation 2a(x- 1)=(5-a)x+3b about x has countless solutions, so a = _ _ _ _ _ _ _ _ _

A: 2a(x- 1)=(5-a)x+3b。

2ax-2a=5x-ax+3b

3ax-5x=2a+3b

x(3a-5)=2a+3b

Equation 2a(x- 1)=(5-a)x+3b There are many solutions to x.

So no matter what value X takes, it always holds.

So this equation has nothing to do with X.

So 3a-5 = 0, 2a+3b = 0.

a=5/3，b= - 10/9

2. What is the sum of all possible four-digit numbers composed of natural number 1 ~ 9, and there are no duplicate numbers?

A: First of all, let's look at a * * *, and how many four digits there are.

There are nine possibilities in a thousand, eight possibilities in a hundred, seven possibilities in ten, and six possibilities in an individual.

A * * * has 3024 four digits.

Look at a seat first. Because every number has an equal status, so

One ninth, that is, 336 units are 1, 336 units are 2, 336 units are 3, ... 336 units are 9.

All these bits add up to 336× (1+2+...+9 )×1.

Look at ten more. Because every number has an equal status, so

One ninth, that is, 336 bits are 1, 336 bits are 2, 336 bits are 3, ... 336 bits are 9.

All these bits add up to 336× (1+2+...+9 )×10.

Look at hundreds more. As can be seen from the above analysis, the sum of all hundreds is 336× (1+2+...+9 )×100.

Look at thousands more. As can be seen from the above analysis, the sum of all thousands is 336× (1+2+...+9 )×1000.

So the sum of all four digits is:

336×( 1+2+...+9)× 1+336×( 1+2+...+9)× 10+336×( 1+2+...+9)× 100+336×( 1+2+...+9)× 1000

=336×( 1+2+...+9)×( 1+ 10+ 100+ 1000)

=336×45× 1 1 1 1

= 16798320

A square table consists of a table top and four legs. 1 m3 of wood can be used to make 50 desktops or 300 legs. There are now 5 cubic meters of wood. How many pieces of wood can be used to make a desktop and how many legs can be used to make a square table?

The speed of the ship in still water is 1 hour 24 kilometers, and the current speed is 2 kilometers per hour. It takes six hours for the ship to go back and forth between A and B. How long does it take to sail downstream from A and from B to A respectively? What is the distance between A and B?

Warehouse A stores 200 tons of coal and warehouse B stores 70 tons. If warehouse A transports 15 tons and warehouse B transports 25 tons every day, how many days later will warehouse B store twice as much coal as warehouse A?

There are 27 workers in Workshop A and 0/9 workers in Workshop B, and now there are 20 new workers. In order to make the number of workers in workshop A twice that in workshop B, how should new workers be assigned to two workshops?

1, assuming that X square tables can be made, then

You need to make x desktops and 4x legs.

x *( 1/50)+4x *( 1/300)= 5

The solution is x= 150.

2. Solution: Let the distance between Party A and Party B be X kilometers.

According to the meaning of the question: x/(24+2)+x/(24-2)=6.

The solution is x=7 1.5.

rule ...........

Three questions

After x days of solution, the stored media is twice that of warehouse A.

Then 2*(200- 15x)=70+25x.

The solution is x=6.

Four questions

If x people are assigned to workshop a, 20-x people will be assigned to workshop B.

According to the meaning of the question, 27+x=2*( 19+20-x)

The solution is x= 17.

1. A two-digit number, where the ten digits are x and the digits are X- 1. What is the two-digit number obtained by exchanging ten digits with digits?

2. The little mother took Mi Yuan to the street to buy food. She spent half on meat and the remaining third on vegetables. So how much money does she have left?

Related answers:

The first question: 1 1X- 10

Question 2: M-m/2-m/2/3= 1/3M yuan.

As shown below, what is the fifth number in line 100?

2 3

4 5 6

7 8 9 10

1 1 12 13 14 15

16 17 ........

The answer is 4955.

From the outermost layer on the left of the graph,1247116, the number after it is always greater than the number before it.

The second ratio is 1 large 1 ... The third is 2 ... The fourth is 3 ... The fifth is 4 ... The sixth is 5. .......... is greater than the fifth, so we can set the nth number of the outermost layer on the left as x, Then x equals [1 plus 2 plus 3 plus < 100. The number of 1 is [1 plus 2 plus 3 plus ... plus < 100- 1 >], which is equal to 495/kloc.

So the fifth number in line 100 is 4955.

1. Calculate the value of1+3+5+7+…+1997+1999.

2. If the value of 2x+|4-5x|+| 1-3x|+4 is a constant, find the conditions that X should meet and the value of this constant.

Third, it is known that

1 2 3

- + - + - = 0 ①

x y z

1 6 5

- - - - - =0 ②

x y z

Try to find the value of-+-+-.

y z x

Fourth, arbitrarily add a "+"or "-"before each number in 1, 2, 3, …, 1998, so is the final result odd or even?

5. A school held a math contest in the first grade, and the number of participants was three times that of those who did not. If the number of students who do not participate is reduced by 6, then the ratio of the number of students who participate to the number of students who do not participate is

2. 1 Ask for the knowledge of participants and non-participants, and the number of junior one students.

Answer: A question:

Original formula = (1+1999) * [(1999-1)/2+

=2000* 1000 /2

= 1000000

Two questions:

If the value of 2x+|4-5x|+| 1-3x|+4 is constant, then

4-5X≥0， 1-3X≤0

So: 1/3≤X≤4/5.

Original formula =2X+4-5X+3X- 1+4=7.

Three questions:

Substitution: 1/X=6/Y+5/Z changed from ② to ①.

8/Y+8/Z=0

Therefore, if Y=-Z is substituted into 1/X=6/Y+5/Z, we get:

1/X= 1/Y

So: X=Y

X/Y+Y/Z+Z/X = 1- 1- 1 =- 1

Four questions:

In 1, 2, 3, …, 1998, * * has 999 odd numbers and 999 even numbers.

No matter the addition or subtraction between two even numbers, the result is even, so only the relationship between odd numbers is considered.

Because the result of addition and subtraction between any two odd numbers is even,

So, in the final analysis, it's all addition and subtraction between odd and even numbers.

So, the final result is very strange.

Five questions:

Suppose the number of people who didn't participate in the competition is X, then the number of people who participated in the competition is 3X, and the total number of students in the whole school is 4X.

If the grade is reduced by 6 students, the total number is 4X-6.

If the number of non-participants increases by 6, the number of non-participants is X+6.

The number of participants is 4X-6-(X+6)=3X- 12.

The ratio of participants to non-participants is 2: 1.

So: 3X- 12=2*(X+6)

Solution: X=24 (people), the number of participants 3X=72, and the total number of students in the whole school 4X=96.

Negative one-half one-third

Negative quarter, negative fifth, negative sixth.

One seventh, one eighth, one ninth and one tenth. . . . . .

What is the seventh number in line 2007 in this group?

The line number of 1 is 1.

There are two numbers in the second line.

There are three numbers in the third line.

....

So there are n numbers in row n,

1 to line 2006, total:

1+2+3+...+2006 = 2006 * 2007/2 = 20 1302 1.

20 1302 1+7=20 13028

The score of the seventh line in 2007 is 1/20 13028.

It is also found that the odd positions of each row are negative.

So the seventh line in 2007 is:-1/20 13028.