A few Olympiad questions, come quickly 15, a few Olympiad problems, come quickly

Number of factors = 2 * 3 * 3 * 2 = 36.

and s=(1+2) (1+3+3) 1+5+5) 1+7)=9672

and 28 The least common factor is 4, so the maximum side length is 4, which can be divided into 11*7=77 blocks.

The least common multiple of and 30 is 150, for every 150 cm walked, the father and son left a total of (150 50) + (150 30)-1 = 7 footprints, 1099 divided by 7 equals 157, total distance = 157*

The number of prime factors = 5 * 4 = 20, and = (1 + 2 + 2 + 2 4) (1 + 3 + 3 +3 ) = 1240

5.The first digit of this three-digit number must be 4, because 469+27 is less than 500, the last digit 0 9 is arbitrary, 480-4-8-0=468, 470-4-7-0=459<460, so the inside () is 8.

180/(y+x)=5

The water flow rate is x=8

180/（t-8）=

The hydrostatic velocity of B is t=32

Turn back time = 180 (t+8) =

Indecisively asked

1.3150 = 2 * 3 * 3 * 5 * 5 * 7, the number of factors: (1 + 1) * (2 + 1) * (2 + 1) * (1 + 1) = 36, the sum of factors:

2.The maximum length of each side is 4 meters (the greatest common divisor of 44 and 28), and it can be divided into 77 pieces (44*28 (4*4)).

3.The least common multiple of 50 and 30 is 150, and for every 150 meters, the father and son leave a total of (150 50) + (150 30)-1 = 7 footprints, and 1099 divided by 7 equals 157,157* meters.

4.432 = 2 * 2 * 2 * 2 * 3 * 3 * 3, the number of factors: (4 + 1) * (3 + 1) = 20, the sum of factors: 1 + 2 + 2 2 3 + 2 4) * (1 + 3 + 3 2 + 3 3) = 31 * 40 = 1240

5.The first digit of this three-digit number must be 4, because 469+27 is less than 500, the last digit 0 9 is arbitrary, 480-4-8-0=468, 470-4-7-0=459<460, so the inside () is 8.

6.The downstream speed of ship A is 36 kmh, the countercurrent speed is 20 kmh, the water velocity is (36-20) 2=8, and the countercurrent speed of ship B is 24 km/h, then the downflow speed of ship B is 24+8*2=40, and the return (downstream) of ship B is 180 40=hours.

Please, ask for an additional bounty...

From the 2 factor, 5+4+3+2+1;

From the 3 factor, 4+3+2+1;

From the 3 factor, 3+2+1;

From the 5 factor, 2+1;

From the 5 factor, 1;

deduct the same 15; 21；35 three, 5 + 15 + 10 + 6 + 3 + 1-3 = 37;

4*11=44；7*4=28；Therefore, the maximum is 4*4,28 pieces.

The least common multiple of 50 and 30 is 150, 150 cm each, the footprints of father and son and 5 + 3-1 = 7, 1099 7 = 157, full length = 157 * 150 = meters;

The sum of its digits does not exceed 9 + 9 + 9 = 27;The three-digit number 46 (), the hundred digit is obviously 4,400+60+? +4 + 10 digits + single digits = 400 + 10 * 10 digits + single digits;

64+？= 9*10 digits; Apparently 72,? =8；Ten digits = 8;

The number inside is 8;

A retrograde 20 kilometers per hour, forward 36 kilometers per hour, water velocity * 2 = 36 - 20 = 16;

Water velocity = 8 km, B retrograde 24 km per hour, forward stroke per hour = 24 + 16 = 40 km, return time = 180 40 = hours.

Number of pieces: (1+1)*(2+1)*(2+1)*(1+1)=36.

SUM: (1+2)*(1+3+3 2)*(1+5+5 2)*(1+7)=3*13*31*8=9672

2.Decompose 44,28 into 44 = 2 * 2 * 11, 28 = 2 * 2 * 7, so the maximum length of each side is 2, and a total of 22 * 14 = 308 pieces can be divided.

30 = 2 * 5 * 3, so every 2 * 5 * 3 * 5 = 150 coincides, let the circumference of this flower bed be x meters: x 30 + x 50 = 1099 + x 150

x=23550

Number of units: (4+1)*(3+1)=20

And: (1+2+2 2+2 3+2 4)*(1+3+3 2+3 3)=31*40=1240

5.Let the three-digit number be xyz, then 100x+10y+z-(x+y+z)=46().

99x+9y=46（）

From the above 46 () must be divisible by 9, so 4 + 6 + () = 9 * i

Because () is 0 9, i=2 and ()=8

One day after the heavy snowfall, the son and the father walked together to measure the circumference of a circular flower garden, their starting point and the direction of walking are exactly the same, the father is 50 cm per step, Xiao Jia is 30 cm per step, because the footprints of the two coincide, so only 1099 footprints are left on the snow, how many meters is the circumference of this flower bed?

Sister won't either, good luck ......ps.I hate math.

Practice Question 1:

Take one serving of grass that one cow eats every day.

The grass eaten by 10 cows in 20 days = the original grass + the grass that was born in 20 days = 10 * 20 = 200 servings of the grass eaten by 15 cows in 10 days = the original grass + the grass that was born in 10 days = 15 * 10 = 150 parts From the above, it can be seen that the grass that is new in 10 days is 200-150 = 50 parts of the new grass growing every day: 50 10 = 5 parts.

The original grass is 200-5*20=100 parts.

Each cow eats 1 portion of grass per day, and first let 5 out of 25 cows eat 5 portions of grass that grows every day, so that the grass that grows every day is eaten up every day, and then just consider how many days the original grass is left by the remaining 20 cows.

100 (25-5) = 5 days.

Note: *=Multiplication = Divide You just need to write the equation in, you don't have to write those words and processes. * and write

Question 1:

1) The grass eaten by 27 cows for 6 days is: 27x6=162 (these 162 days include the original grass of the pasture and the grass that grows new in 6 days) (2) The grass eaten by 23 cows for 9 days is: 23x9=207 (the 207 days include the grass that grows in the pasture and the grass that grows in the pasture for 9 days) (3) 1 The grass that grows new in one day is:

207--162) divided by (9--6) = 15 (4) The original grass on the pasture is:

27x6--15x6=72

5) The new grass grows every day is enough for 15 cows, 21 cows minus 15, and the remaining 6 eat the grass of the original pasture:

72 divided by (21--15) = 12 (days).

Therefore, it takes 12 days to raise 21 cows to eat the grass on the pasture.

2. When a boat found that it was leaking, it had already entered some water, and the water entered the boat at a uniform speed. If 10 people are digging for water, it will be done in 3 hours; For example, 5 people will wash the water in 8 hours. If it is required to be finished in 2 hours, how many people should be arranged to wash the water?

Answer: Set up 1 person to wash water one per hour.

5 8-10 3) (8-3) = 4 (parts) (10-4) * 3 = 18 (parts).

18 2 + 4 = 13 people.

Take the first question as an example:

Let the grassland have a, grow x every week, and eat y per cow every week

There are two conditions that can be used to list the equations:

a+6x=27*6y

a+9x=23*9y: a=72y x=15y, now find z: a+zx=21*zy, substitute a, x, eliminate y, you can calculate z is equal to 12 weeks.

All other questions are the same, and the answers can be obtained by modifying the meaning of the equations and unknowns accordingly.

1. There is a rule, the first line has no intersection point, the second line can only have one intersection point with the first one, and the third line can only form a maximum of two intersection points with the two existing straight lines, so the maximum should be: 0 + 1 + 2 + 3 +...n-1)

1.Set spinach x acres, then cabbage 21-x acres.

So the solution is x=6, so the cabbage is 15 acres.

2.Let clothing A x, then clothing B is 80-x

then 45x+50(80-x)=3800

The solution is x=40, and the b garment is 40

3.A and B cooperated for 4 days to do this project, 4 * (1 12 + 1 20) = 8 15, leaving 1-8 15 = 7 15

Therefore, C needs to be done separately by (7 15) divided by (1 15) = 7 days, if you understand the steps, you can ask questions.

1 Set spinach x acres and cabbage y acres.

x+y=21

x=6 y=15

2 Set A x set B Y set.

x+y=80

45x+50y=3800

x=40 y=40

3 A completes the project 1 12 in one day, B completes all the works in one day, 1 20, and C completes all 1 15 in one day

A and B cooperate in 4 days to complete all (1 12 + 1 20)x4 = 8 15 B and C cooperation to complete in one day 1 20 + 1 15 = 7 60, so the remaining number of days to complete is (7 15) (7 60) = 4 B works for 8 days.

1.Set up x acres of spinach and y acres of cabbage.

x+y=21

The solution is x=6 and y=15

2.Set up A fashion x set, B fashion Y set.

x+y=80

45x+50y=3800

The solution is x=3Set up B and C cooperation x days.

Then 4(1 12+1 20)+x(1 20+1 15)=1x=4So, B's working time is 4+4=8 days.

, add three numbers after 917 to form a six-digit number, so that it is divisible, then the maximum and minimum of the six-digit number are few.

Maximum 917970

Min. 917010

I can't write an equation.

2. Use the three methods to identify whether the equation is 12345678 multiplied by 7 = 86419646 is true: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

12345678 divisible by three.

86419646 is not divisible by three.

Therefore 12345678 multiplication by 7 = 86419646 does not hold 3, ( 2000 ( ) is divisible by , such numbers are those, and if the last three digits are multiples of 8, then this number is a multiple of 8 (so the last parenthesis is filled with 8 or 0).

The sum of the digits is divisible by 9, and this number is divisible by 9, so n=8,7

This number is 820008 or 720,000

1. The last digit of a number divisible by 2 and 5 at the same time must be 0, and the sum of the digits of a number divisible by 3 is a multiple of 3, and the other two digits are a and b

Because 9 + 1 + 7 = 17, and 0 a + b 18

So the sum of the six-digit digits is between 17 and 35, where the maximum divisible by 3 is 33 and the smallest is 18, and A+B is 1 and 16 respectively

So the maximum of this six-digit number is 917970 and the minimum is 917010

2. The characteristic of a number divisible by 3 is that the sum of the digits of this number is divisible by 3.

In the multiplication to the left of the equal sign, the 12345678 is a multiple of 3, so the number on the left must be a multiple of 3, and the sum of the numbers on the right 86419646 is 44, not a multiple of 3, so the number on the right is not a multiple of 3 86419646, so this equation does not hold.

3. The characteristic of a number divisible by 8 is that the last three digits are divisible by 8, so the last digit of this number can only be 8 or 0, and the number that is divisible by 9 is characterized by the sum of all numbers divisible by 9, so if the first digit is x, then the sum of x+2+8 can be divisible by 9, or the sum of x+2 can be divisible by 9.

So such numbers have 820008 and 720,000

1: If this number is to be divisible, then it must be divisible by 30. Minimum: 917010 Max: 910970

Let the six digits be 917abc

The single digit divisible by 25 must be 0

c=0 is divisible by three, and the sum of the bits is divisible by three.

9+1+7+a+b+0

17+a+b

A+B is at least 1

The smallest six-digit number is 917010

Because a b is between 0 and 9.

So A+B won't go more than 18

Let's count down from 18.

17+16=33 is divisible by 3.

The combination of 16 has 97, 88, 79

The largest number is 97

So the maximum six-digit number is 917970

Answer: The largest number is 917970, and the smallest number is 9179010 second, 1+2+3+4+5+6+7+8=36 can be divisible by 3, 8+6+4+1+9+6+4+6=44, and is not divisible by 3, so this formula must be wrong.

The third question ()2000( ) is divisible by .

Let this number be a2000b

Divisible by 9.

Then a multiple of a+b+2=9.

ab is less than 9.

So A+B won't go more than 18

Then a+b+2=18

or a+b+2=9

If a+b=16

It can be divisible by 8, so the single digit b is 0, 2, 4, 6, 8, then it can only be when.

a=8 b=8

Then this number is.

If a+b=7

Then there is a=7 b=0

a=1 b=6

a=3 b=4

a=5 b=2

Revalidation 120006 Not divisible by 8

320004 is not divisible by 8.

520002 is not divisible by 8.

720000 fits the topic.

So there are 720,000 820008