Olympiad Questions: Help, Olympiad Questions: Help

1, in fact, it should be calculated, the sum of these natural numbers is divided by 7 and then divided by 7, and the integer is divided by 7, the remainder can only be 1-6, in the question, the decimal point is 2, then this remainder should be 2, so if it is rounded, then it should be, otherwise it is.

2.In fact, it is to find a number, just so that this number and the five numbers in the problem have the same number at least one position, and then arrange it.

Start with each and find the number that appears the most, which is 5 or 4 if you choose 5 first

Then, there is still left.

Obviously, in this case, the ten and hundred digits of the three numbers do not want to be the same, and there is no number that matches the topic.

Then select the single digit to 4, then it is left.

925 Thus, the ten is 2

The hundred is 7, so this is a decade 724

3. This is relatively simple, let the fruit candy be x kg, and the butterscotch candy will be y kg, then the weight after mixing is x+y kg

Also, the total sales of the blend and the sum of the two sugars remain unchanged. And so it goes.

So x:y=35:3

Regression: Let x be 1-9 and take the natural number 212

Exhaustive elimination is assumed 5 times.

A If the first digit takes 8, then the third digit must not be 4, then the second digit is known from 364 that the second digit is 6, so it is 863

There is no correspondence to 925, so it is wrong. Proceed with the assumptions.

b take 7, 724

The total production volume: 25 * 30 = 750 pieces, 25 * 6 = 150 pieces have been produced, and the remaining 750-150 = 600 pieces. It is required to be completed 4 days in advance, that is, a total of 30-4 = 26 days are required to be completed, 6 days have been processed, and 20 days have to be worked, that is, the remaining 600 pieces are completed in 20 days, and 600 20 = 30 pieces.

Think of the distance between A and B as the unit "1".

A bus that comes every 6 minutes to get to a place is a meeting between the bus and someone, and the speed sum is 1 6 6 6/1

Every 12 minutes, a bus to B goes to place B, and the bus is chasing someone, and the speed difference is 1 1 12 12 12 times

The speed of the bus is (1/6 1/12) 2 1/8 The interval departure time of the bus is 1 1/8 8 minutes.

Let the walking speed of the person x the speed of the vehicle y and the departure time t at intervals, then:

12x=y(12-t)

6x=y(t-6)

The two formulas are divided.

2=(12-t)/(t-6)t=8

A 3-digit number, after the exchange of single digits and hundreds of digits, it is still a 3-digit number, and the difference between it and the original 3 digits gets a single digit is 7, try to find what is the difference between them?

The original question is something like the one above!

The difference between the swapped three-digit number and the original three-digit number is a multiple of 9.

Let's deduce, let the original three-digit number be ABC, and the new three-digit number is CBA, assuming that the original three-digit number is larger, just a c, then there is abc-cba=(100a-a)-(100c-c)(10b-10b)=99(a-c).

Then we can know that the ten digits of the difference must be 9, and the sum of the digits of the multiple of 9 is a multiple of 9, so the hundred digit of the difference is 2, so the difference is 297

Analysis and solution: Let the original three-digit number be ABC, then the three-digit number obtained after the exchange of single digits and hundreds of digits is CBA, and their difference vertical form is:

a b c c b a

As can be seen from the above vertical type, A is larger than C, and the difference between 10 and C and A is 7, so it can be seen that C and A can only be the following cases: 1 and 4, 2 and 5, 3 and 6, 4 and 7, 5 and 8, 6 and 9. In these cases, A and C are 3 different, then, taking into account the borrowing, the difference between the above vertical can only be 297.

There is a problem with the question you provided. Read it for yourself.

There seems to be a problem with the title, please make it clear!

What does the title mean???

Your topic is not valid!!

Set x classmates. Total 4x+4 capsules and skew.

4x+8 is divisible by x.

So 8 is divisible by x.

So, x 1, 2, 4, 8

Since if the average score is given to the students, there are 4 fewer grains, 1, 2, and 4 are all divisible by 4, so x can only be 8

8 students, 8*4+4 36 sugars.

1。Crickets are 6-legged and spiders are 8-legged, and there are more crickets than spiders.

46 (6+8)=3 remainder is not an integer.

46 (6+8) = 2 remainders, so 5 crickets, 2 spiders.

46 (6+8)=1 remainder is not an integer.

2。Set up x horses, y mares, and z horses.

Formula 1 3x+2y+1 2z=100 to get an even number of z.

Equation 2 x+y+z=100, subtract z, and get 5x+3y=100, because y is greater than 20. Then the value of y is 20, 25, 30, and the corresponding x is 8, 5, 2, and the value of z is 72, 70, 68. The big horse may be 8, 5, 2, 20, 25, 30 for the mare, and 72, 70, 68 for the pony.

These two problems are obviously indefinite equations.

1.The spider has 8 legs, the cricket has 6, the cricket x and the spider y have the equation: 6x+8y=46

Obtains: when x=5, y=2; When x=1, y=5

So there are 5 crickets and 2 spiders. Or 1 cricket and 5 spiders.

2。Set up x horses, y mares, and z horses.

Get the system of equations:

3x+2y+1 2z=100 to get an even number of z.

x+y+z=100, subtract z, and get 5x+3y=100, because y is greater than 20. Then the value of y is 20, 25, 30, and the corresponding x is 8, 5, 2, and the value of z is 72, 70, 68. The big horse may be 8, 5, 2, 20, 25, 30 for the mare, and 72, 70, 68 for the pony.

1) 46 6 = 7 remainder 4; 8-6=2；4/2=2；7-2=5；5 crickets, 2 spiders.

2) Big horse x, mare y, pony z: x + y + z = 100;3x+2y+1/2z=100；y+5/2z=200，5x+3y=100；z=80-2/5y，x=20-3/5y；y is a multiple of 5 and less than 35, y is not less than 20, and y is one of them; Therefore, the corresponding x takes ,

2 in one, z takes one in one;

When there are 20 mares, 8 large horses and 72 small horses;

When there are 25 mares, 5 large horses and 70 small horses;

When there are 30 mares, 2 large horses and 68 small ponies;

1.Master Li processed a batch of parts and completed one-fifth of the total tasks on the first day The second day completed one-third of the remaining tasks The second day completed 20 more parts than the first day How many parts are there in this batch?

300 pcs. 2.There are two ropes of the same length The first one is cut off by a third and the second is cut off by two-fifths The remaining part of the two ropes is six and a third meters long How many meters is cut off by the first rope?

6 and 1 3 (1-1 3+1-2 5).

5 m 3A and B have a total of 420 books on the two shelves If you put one-fifth of the books on the A bookshelf into the B bookshelf, then the ratio of books to the two bookshelves A and B is 3:4 How many books did the A bookshelf originally have?

225 copies. 4.Dongfeng Elementary School has a number of students It is known that there are 5 fewer boys than 5/9 of the total number of students in the school 11 more girls than 3/7 of the total number of students in the school How many students are there in the school?

378 people. 5.The grain store brought in a batch of flour, and on the first day it sold three-eighths of all of it, and the next day it sold five tons, and then exactly five-sevenths of the flour was sold, and how much flour was left?

70 tons. 6.There were a number of balls in the bag, and the red balls were 5/12, and then eight red balls were put into the bag, and the red balls were half of the total, and it turned out that there were many red balls in the bag.

20 pcs. 7.If 22 tons of grain are taken out from warehouse A and put into warehouse B, then the grain stored in warehouse B is 2 3 times that of warehouse A, how many tons of grain are stored in the two warehouses?

1 and 1 3 = 4 3

770 tons. 8.There are 615 students in Yuhong Elementary School, and it is known that one-half of the number of students in the sixth grade is equal to two-fifths of the number of students in the fifth grade, and it is also equal to three-sevenths of the number of students in the fourth grade.

6th grade 615 (1+1 2 2 5+1 2 3 7).

180 people. 5th grade 180 1 2 2 5

225 people. Fourth grade 180 1 2 3 7

210 people. 9.Processing a batch of parts If there is a A and B processing together, it takes 3 hours to process together, it takes 4 hours to process by A and C together, it is known that it takes 8 hours to process by B alone, C can process 50 parts per hour, how many parts are in this batch?

1200 pcs.

10.A project takes 20 hours to do alone, B takes 24 hours, C takes 30 hours, and now the three of them are working together, but A quits halfway through the process, and it takes 14 hours to complete the task, how many hours does A do?

5 hours.