Olympiad Problem Solving, Problems and Answers, Math Olympiad Problem Solving

1.Type B (9+9) (4-1) = 6 yuan.

Class A 6 * 4 = 24 yuan.

Household. 42 + 26-54 = 14 households.

1.B's original unit price is: (9+9) (4-1)=6, and A turns out to be 24 yuan.

2.68-14=54, Raising chickens and ducks: 42+26-54=14

Specialized chickens: 42-14=28 homes.

Topic 1: The unit price of goods A is 9 2 = 18 yuan more than that of goods B.

The unit price of goods B is 18 (4-1) = 6 yuan.

The unit price of goods A is 6 + 18 = 24 yuan.

Topic 2: There are 68-14-26=28 households that specialize in raising chickens.

The dolphin worked for 10 days, and the whale only paid it 20 Ocean Coins and 1 Pearl, so if it worked for 30 days, it should get 20 * (30 10) = 60 Ocean Coins and 1 * (30 10) = 3 Pearls.

Therefore, one pearl is worth (100-60) (3-1) = 20 Ocean Coins.

20 Ocean Coins and 1 Pearl for 10 days, 60 Ocean Coins and 3 Pearl for 30 days.

So this pearl is worth 20 Ocean Coins?

Give him 20 Ocean Coins and 1 pearl after 10 days of drying, which means that after 30 days of drying, you can give it to him.

60 Ocean Coins and 3 Pearls.

The title also says that after 30 days, the whale will give the dolphin 100 ocean coins and 1 pearl, so 2 pearls are equivalent to 40 ocean coins.

So, this pearl is worth 40 divided by 2 equals 20 Ocean Coins.

Let one pearl equal x ocean coins.

then the 30-day salary is 100+x Ocean Coins.

The 10-day wage is (100+x) 3=20+x

Solution x=20

Let the pearl be worth x ocean coins, then.

100+x）/3 = 20 + x

100 + x = 60 + 3x

Solution x=20

So, this pearl is equal to 20 Ocean Coins.

Let the length of time from walking to the specified time be t, and the total distance is s, then 3*(t+2 3)=s

6*(t-2 bucket void 3)=s

Get. t=2 s=8

If the empty line arrives on time, the speed of the line is s t = 8 2 = 4 km h

No. 11, assuming that we take 1 for the first time, the interval between the first time is 2, the interval between the second time is 4, the third time is 8, the fourth time is 16, the fifth time is 32, and the fifth time is 32, 32, 64, 96 is taken out of 32, 96, and 64 is left, which is 10 different from 74, that is to say, the 1st number I took at the beginning should be 10 backwards, that is, the 11th chess piece.

If you start with 1, the last remaining one is 64 side states.

Now the remaining remnants of the erection are 74, 74-64=10

Then the first time it is taken is: 1 + 10 = 11.

If all three prime numbers are odd.

then the sum is an odd number.

Therefore, there is a prime number that is an even number of Zen teasing.

i.e. = 2 so the sum of the other two = 78

The closer they are, the greater the product.

The closest lead limb is 37 + 41 = 78

So the maximum product is 2*37*41=3034

Let's say you take a lap and come over for a round.

Assuming that the first one is numbered 1 and the rest are all odd, then the first round will end up with number 99, leaving 50.

At this time, the second round begins, because the first round finally takes the number 99, so the second round takes the first 2, and the rest takes the number divided by 2 to get the odd number, and the second round finally takes the number 98, leaving 25.

At the beginning of the third round, the last one taken in the second round is 98, and there is a number 100 after 98, so the first one in the third round is 4, and then all the ones are divisible by 4 and are odd, so the last thing taken in the third round is 100,. And 12 remain.

At the beginning of the fourth round, the last one taken from the third round of hail is 100, and the last one taken after the third round of 100 is 8, so the first one in the fourth round is the number after 8, that is, from the pure balance 16, and then each one taken is divisible by 8 and is even. The last to be taken was 96. 6 left.

8, 24, 40, 56, 72, 88, respectively

At the beginning of the fifth round, the fourth round takes 96 at the end, and 96 is followed by 8, so the fifth round starts to take the digit behind the number 8, that is, 24, so the fifth round takes the number 24, 56, 88So there are 8,40,72 left

At the beginning of the sixth round, the last to take 88 in the fifth round is 88, and 88 is followed by 8, so the first one in the sixth round is 40 after 8Then, it's time for the next round.

In the seventh round, since the post-40s were taken away, there were 72 after the 40s, so the seventh round took away the post-72 one, that is, 8, so in the end the number 72 remained

From the above, the first one to take away is the number one, and the last number 72 is left, in order to get the number 74, since 74 = 72 + 2.

So the first one to take should be 1+2=3, that is, the first one to take is number 3

Question 9: (There should be 5 grades).

Question: 1st grade + 2nd grade + 4th grade + 5th grade = 25 1st grade + 2nd grade + 3rd grade + 5th grade = 19

3rd Grade + 4th Grade = 8

Question 12: 2 questions are answered incorrectly and 8 questions are answered correctly.

13 questions. Rope length (80+70) (1 2-1 3) = 900cm, 900 3 + 70 = 370cm

Question 1:

430 (units).

Question 2: 1200 30 = 40 (minutes).

1200 60 = 20 (minutes).

40 (m) Question 3: Same as above. Question 4:

25 (years old) There are too many questions and not enough time, so I will answer the rest of the questions next time.

Classmates, these questions shouldn't be Olympiad questions, they're not difficult, you should be able to do them, you sent too much, just say two to you.

1. The bicycle factory produced a total of 4,500 bicycles in the first 10 days of April and 8,400 bicycles in the next 20 days. How many bikes are produced per day on average this month?

April is 30 days.

2. Xiao Wang carried out mountain climbing exercises, when he went up the mountain, he walked a total of 1200 meters, walked 30 meters per minute, and when he went down the mountain, he returned along the original road, walked 60 meters per minute, and asked Xiao Wang to go up and down the mountain at an average speed.

Ascent time: 1200 30 40 minutes.

Descent time: 1200 60 20 minutes.

Average speed: 2400 60 40

Even if it's a sixth grade, there are a lot of questions, tot, I'll help you answer them one by one!

1. (4500 + 8400) divided by 30 is equal to divided by 60 is equal to 20 1200 divided by (60 + 20) (the answer is calculated by yourself) 3.

Multiply by 2-19 - (25 + 23) + 19 = 11 people.

18-(36-4) = 10 people.

2+1=5 minutes.

10. Set up x science and technology books.

x+48=3xx=24 copies.

72 fairy tale books 24 science and technology books 11: Let him answer x questions correctly 10x—2(10-x)=76 get x=8

12. Set the rope x cm 1 2x-80=1 3x+70 to get x=900 that is, 9 meters.

Tot is tired of me, can you choose me?

(16) 65 and 115 copies.

17) 175, 150 and 130.

18) 999 pcs.

19) 200, 400 and 800 trees.

20) 8 days.

Just use the equation to solve it.

1 3 x 9 = cubic decimeter, i.e. litres per hour, leakage of 8 litre-hours.

A:"It takes 8 hours for all the sand in the hourglass to flow out".

Volume = 4 4 cubic decimeters = liters.

Time = Hours.

4 dm = m 9 dm = m then volume v = 1 3 * (

Time is equal to v 8=hours.

As 1 knows, Sanniu is not a bakery owner. 3 know that Sanniu is not a company employee. By 4 know that Sanniu is not a barber. By 5 know that Sanniu is not a butcher shop owner. Therefore, Sanniu can only be a tobacco and alcohol dealer.

Sigui is not a bakery owner, not a tobacco and alcohol dealer, not a hairdresser, and you know, Sigui is not a company employee, so Sigui is a butcher shop owner.

You 3 know that Wuwa is not a company employee, and 6 knows that Wuwa is not a hairdresser, and in addition, Wuwa is not a tobacco and alcohol dealer, not a butcher shop owner, so Wuwa is a bakery owner.

Erhu is not a tobacco and alcohol dealer, not a butcher shop owner, not a bakery owner, and it can be seen from 4 that Erhu is not a barber, so Erhu can only be a company employee.

Dalang is not a tobacco and alcohol dealer, not a butcher shop owner, not a bakery owner, not a company employee, so Dalang is a barber.

May mine be of help to you! If you have any questions, please ask and be willing to answer them. If you understand and solve your problem, please answer it in time! If you have other questions, click to ask me for help after this question, it is not easy to answer the question, please understand, thank you.

Solution: Ling Dalang, Erhu, Sanniu, Sigui, Wuwa and five people are numbered respectively, and the five occupations of bakery owner, barber, butcher shop owner, tobacco and alcohol dealer and company employee are numbered A, B, C, D, and E respectively.

You can list a ** to show who can't be what occupation (for example, if Dalang can't be a bakery, draw a " " on the column with 1 and a).

Then from the title, you can draw:

First of all, it can be directly concluded from row B and column that Dalang is a barber, Sanniu is a tobacco and alcohol dealer, and Sigui is a butcher shop owner.

Therefore, Erhu and Wuwa are company employees and bakery owners.

And because the schematic diagram shows that Wuwa is not a company employee, Erhu is a company employee and Wuwa is a bakery owner.

Therefore, Da Lang is a barber, Erhu is a company employee, Sanniu is a tobacco and alcohol dealer, Sigui is a butcher shop owner, and Wuwa is a bakery owner.

Hope, thank you!

From the two conditions, it can be seen that Da Lang is a barber; From several conditions, it can be seen that Sanniu opened a tobacco and alcohol dealership; The remaining three are not sufficiently qualified to judge.

Daro is a hairdresser.

Erhu tobacco and alcohol.

Sanniu Company Employee.

Four expensive butcher shop owners.

Wuwa bakery owner.

Bakery: Five Baby.

Barbershop: Da Lang.

Butcher's shop: four expensive.

Tobacco and alcohol dealers: Sanniu.

Company Employee: Erhu.

Set the purchase price as: bettor x yuan.

Equation: (x*.)

The solution is x=140

So the store earned 168-140=28 (yuan).

It shows that the foundation of the store is not credible!

Not credible. Calculate the list price of 168

The price of the world is 210 according to the merchant

This has already made 28 slag by searching for rent slag.

Assuming that the original price is x yuan, then the smile is x=140

So the buyer earned 168-140=28 yuan.

Therefore, the store's claim is not credible.

List price: 168 yuan).

Cost: 210 (1+RMB).

According to the merchant, the cost is: 168-10 = 158 (yuan) and envy is more lead-resistant: Changpai is good 158-140 = 18 (yuan), so the merchant's statement is not credible.