Mathematics Competition Questions Primary School Level 100 points Reward

If all seven coins are turned face up, the sum of the times the seven coins are turned should be the sum of seven odd numbers, but by turning six of the seven coins at a time, no matter how many times they are turned, the sum of the times is still the sum of several even numbers, so the requirement in the question cannot be achieved

No. On the one hand, it takes an odd number of times for each coin to flip from heads to tails, such as 1, 3, 5 ,......

7 coins are flipped from heads to tails, and the 7 odd numbers are added together, and an odd number is required for a total of odd times.

On the other hand, 6 pieces are flipped each time, and an even number of times are flipped and no matter how many times they are flipped they are, the sum is an even number of times.

So you can't make the tails of the 7 coins face up.

No. Let the coin face face be 1 and the back side 0At the beginning, the total value is 7, and the target should be 0 according to the rules

But no matter how you flip it, according to the rules, the value that comes out every time is +6, +4, +2, +0, -2, -4, -6 on the original value, all of which are even.

i.e. 7+(..)All values in the above) = 7 + even = odd cannot be equal to zero. So.

No. The action of turning 6 pieces each time is equivalent to two steps:

1.Flip one of them;

2.All of them are turned upside down.

Counterproof: Suppose that after turning N times, all are negatives.

Since 1 and 2 are independent. Because in the first step, each piece must be turned over to get to the reverse side, so n must be a multiple of 7 to be consistent on all sides, that is, n=m*7;

In addition, for each flip, the second step is to flip all the coins over.

Therefore, n+m must be an odd number.

m*7 + m = m*8, cannot be odd.

So let's assume failure.

Proof can't.

1 is positive, 2 is negative.

After that, it is 1 2 2 2 2 2 2 2 1 1 1 1 1 1 2....

So the requirements in the title cannot be fulfilled.

It can't be done. For the first time, 6 anti.

The second time 0 anti or 2 anti.

The third time 4 anti or 6 anti.

Fourth, 2 anti or 4 anti.

Looped.

No, seven are facing up, turning six, not at all, odd numbers are turning even numbers, remember.

I really want to know the answer soon, what an interesting question.

I'm in sixth grade.

Elementary school mathematics cannot use functions, only addition, subtraction, multiplication and division. This question is done backwards:

For every 1 question that is wrong, 5 points are not allowed, 3 points are deducted, and the loss of points for each question is 5 + 3 = 8 points, and Xiaogang loses a total of 100-76 = 24 points.

So Xiao Ganggong made 24 8 = 3 questions wrong.

The number of questions that Xiaogang did correctly is: 20-3=17.

Chickens and rabbits in the same cage:

Number of questions done incorrectly: 5*20-76) (5+3)=3 questions.

Number of questions to get right: 20-3=17.

Method 1:

Set x correctly, wrong (20-x).

5x-3（20-x）=76

x=17Answer: 17 true.

Method 2: If each question is correct (i.e. full score), it is 20*5=100 points.

But only 76 points, minus 100-76 = 24 points.

Why are there any points lost? Obviously, I answered the wrong question, and 3 points for the wrong question were to be subtracted, but the 5 points I deserved were gone, so 8 points were subtracted.

There are 24 8=3 questions answered incorrectly.

20-3=17 questions answered correctly.

If you weren't in elementary school, you could easily get a 2-yuan equation and get 17 true and 3 wrong.

In elementary school, I don't know if my solution is suitable for it:

Xiao Gang did every question, that is, he did a total of 20 questions and scored 76 points, using the compromise method, if only half of them are right, then it is only 50 points, and Xiao Gang is 76 points, so the number of questions that are correct must be greater than 10; In the compromise, if you answer 15 questions correctly, it is only 75, so it must be greater than 15 questions; The range is only 16-19, and then substitute the operation one by one, and verify to get the correct answer.

Set the correct questions, because Xiao Gang did every question, so he got the wrong (20-) questions. From the meaning of the title:

Answer: I got 17 questions right.

Set the correct x question and the wrong y question:

x+y=20 Because Xiaogang did 5x-3y=76 for each question

So x=17 y=3

That is, 17 questions were done correctly.

Xiao Gang did all the questions.

Let's say Xiaogang did x questions correctly and got (20-x) wrong (5x-3(20-x)=76

5x-60+3x=76

8x=136

x=17Answer: Xiao Gang did 17 things correctly.

If the x channel is right, then the wrong 20-x lane.

x*5-(20-x)*3=76

So x=17

Solution: Let's say Xiaogang did x questions correctly and got (20-x) questions wrong.

5x-3(20-x)=76

5x-60+3x=76

8x-60=76

8x=76+60

x=136÷8

x=17Answer: Xiao Gang got 17 questions right.

Set x questions correctly, because Xiao Gang did every question, so he got the wrong question.

From the inscription: 5x-3=76

5x-60+3x=76

8x=136

x=17Answer: 17 questions correct.

If you get all the questions right, the score is: 5*20=100 (points), answering one question incorrectly is equivalent to deducting 8 points from the total score.

Because 100-76 = 24

So I got 3 questions wrong.

Answer: I got 17 questions right.

Assuming that all are correct, 20 5 = 100 points should be awarded, which is 100-76 = 24 points worse than the actual one, because the difference between doing a wrong question and doing a correct question is 5 + 3 = 8 points, 24 is a multiple of 8, and 24 8 = 3 questions are wrong.

20-3=17 questions to get right.

If the x path is right, the wrong (20-x) lane.

3*（20-x）+5x=76

x=17So, 17 answers correctly.

Test: 17*5+(20-17)*(3)=76

You can get 5 points for doing 1 question correctly, assuming that Xiaogang is all right, you can get 20 times 5 equals 100 points, because you get 5 points for doing 1 question correctly and 3 points for doing a wrong question, that is, the difference between the score difference between 1 question and 1 question is 5 3 equals 8 points, and Xiao Gang's actual score is 24 points less than 100 points, and the reason for 24 points less is because Xiao Gang did 24 8 3 questions wrong. Therefore, Xiaogang did 20 minus 3 correctly equals 17 questions.

Suppose you get all 20 questions right, you should get 100 points, but you only get 76 points, so the number of questions you get wrong is.

100-76) (5+3) = 3, so you got 7 questions right.

5 points are awarded for each correct question, and 100 points are awarded for 20 correct questions. 3 points will be deducted for each wrong question. This is equivalent to a loss of 8 points (5 points and 3 deductions), and Xiaogang scored 76 points and lost 24 points.

24/8=3.I got exactly 3 questions wrong. So Xiao Gang got 17 questions right.

20 5 equals 100 points, 100-76 equals 24 points, 5+3 equals 8 points, 24 divided by 8 equals 3 lanes, 20-2 equals 17 lanes.

Because it takes 12 hours for the hour hand to go in one circle.

At this point, the minute hand has gone 12 times.

2008 12 4

So the minute hand goes 2008 laps the same as 4 turns.

i.e. walked for 4 hours.

So it's 2 points.

One revolution of the minute hand is one hour, 2008 is 2008 hours, and there are 24 hours in a day 2008 24 = 83 ......16

That is, 10 + 16 = 26

26-24 = 2 points.

When the minute hand turns 2008 times, the minute hand turns 1 circle for 1 hour, that is, the hour hand has gone for 2008 hours, based on 10 o'clock, 12 hours a round, 2008 12 rounds - 167 rounds * 12, which is about equal to 4 hours (based on ten o'clock); So when the minute hand turns 2008, it is 2 o'clock (based on 12 o'clock).

The minute hand turns in 1 hour, 2008 laps is 2008 hours, 24 hours a day, with 2008 24 to get 83 days and 16 hours left, which means that after 83 days, it still needs to rotate 16 times, in the 14 revolutions it is 24 o'clock in the evening, that is, it is early morning, and the remaining two turns are 2 o'clock in the morning.

2008/24=83...The remainder is 16, so 10 o'clock plus 16 time to push forward 16 is 2 o'clock in the morning.

200 8 12 = 167 (circle) surplus 4

10+4---12=2.

It should be 2 p.m.

2008/24=83...16 10 + 16 = 26 26-24 = 2 at 2 o'clock in the morning.

2008 24 Must be rounded out and cannot be reduced.

The minute hand turns once and the hour hand goes a little. The minute hand turns 12 times and the hour hand turns once. 2008 divided by 12 is 4, so it's 2 points.

It's still the same location, it's still 10 o'clock.

1 .Divide the three-meter-long steel bar into five sections, each section is the full length, [1 5], is [m], and this length is [3 5] of one meter.

2.Li Hua originally planned to complete the work in 12 hours, but it was completed in 10 hours, and his work efficiency increased by [20] compared with the original plan.

3.The unit of 55 percent of the fraction is 1 100, and adding 145 such units is the smallest prime number.

5.There are 48 people in the 61 class today, one person each on sick and personal leave, and the attendance rate of the class today is [96%].

6.In a subtraction equation, the sum of the subtracted and subtracted is equal to 240, and the difference is 2 times the time difference of the subtraction, and the difference is [40].

7.Fill in the numbers in the squares, make up the numbers, and calculate them according to the regulations.

As; [10] take [9] stable minus [7] upper [eight] lower is equal to [three] position [one] body, [109 minus 78 equals 31].

1] knife [2] paragraph multiplication [3] character scripture is equal to [3] head [6] arm, 8] face majesty multiply [7] seven orifices smoke is equal to [5] face [6] color, [8 7 56].

Ten years of trees multiplied by [hundred] years of trees is equal to each has [ thousand ] autumn [ 10 100 1000 ]

9] Xiaoyun outside minus [1] is equal to [8] face exquisite, [9-1 8].

8.A restaurant can make a square table for 4 people, and if there are more than 4 people, the restaurant owner will put the table together to make a person; If you know the number of tables in a row, how many people can be made, please use a relational expression to express your method. 【 3-1)n 】。

The 172 RMB consists of at least 4 banknotes.

9.The bookstore sold a total of 120 copies of two kinds of books, five yuan for each book of type A and yuan for book B, and the number of books sold in type A was more than that of type B, and the number of books sold in type A was more than that of type B, and the number of books sold in type A was [70] copies. Ann law added numbers; 1 4 13 40 121 ［ 364 ］1093 ．．

10 It takes 6 minutes to make a piece of wood into three sections, and it takes [9 ] minutes to make it into four sections a8

1. One-fifth, three-fifths meters, three-fifths.

145 pcs. 7, one, two, three, three, six, 12 times 3 equals 36 eight, seven, five, six, 8 times 7 equals 56

Ten, hundred, thousand, 10 times 100 equals 1000

Nine, one, eight, 9 minus 1 equals 8

1 The school has held three competitions in mathematics, composition and nature, and 25 students in a class have signed up to participate. Among them, 14 participated in the mathematics competition, 12 participated in the composition competition, 10 participated in the nature competition, and 4 participated in the mathematics composition competition, and 2 participated in the mathematics and nature competition. Only one person participated in all three competitions. Q: How many people participate in the essay and nature competitions?

4 people. 2 One day after a heavy snowfall, Xiao Ming and his father walked together to measure the circumference of a circular garden. They started from the same point and went in exactly the same direction.

Xiao Ming's average step length is 54 cm, Dad's average step length is 72 cm, because the footprints of the two overlap, and they returned to the starting point after walking a circle, leaving only 60 footprints on the snow. What is the circumference of this garden?

The distance they took from the starting point to the first time the footprints coincided This distance is a multiple of Xiao Ming and Dad's step length, and it coincides for the first time, so this distance is the least common multiple of their step length The least common multiple of 54 and 72 is 216, from the starting point to the first time the footprints coincide: Xiao Ming's footprints are 216 54 = 4 (pieces), and Dad's footprints are 216 72 = 3 (pieces) Because the two of them have a footprint that coincides, So there are a total of footprints (4+3-1) = 6 (pieces) in this 216 cm long journey.

And because 60 6 = 10, 216 10 = 2160 (cm).

So the circumference of this parterre is meters.

3.A and B walk in opposite directions from two places 1,100 meters apart, A walks 65 meters per minute, B walks 75 meters per minute, and B starts to set off only 4 minutes after A departs. B takes a dog and B sets off at the same time, the dog runs towards A at a speed of 150 meters per minute, immediately turns back and runs towards B after encountering A, and then turns back to run towards A after meeting B, and the dog does not stop until A and B meet.

How far did this dog run?

4 minutes after A's departure, the two were 1100-65*4=840 meters apart.

After B's departure, the time they meet is: 840 (65+75)=6 minutes.

The dog has been running for 6 minutes, and the distance he has run is: 150 6 = 900 meters.

So the dog ran a total of 900 meters.

4.A boat sails 20 kilometers per hour in still water, and in the river with a current speed of 4 kilometers per hour, it takes a shared hour to travel between piers A and B, and the distance between piers A and B is found.

Answering and detailed answering process.

Downstream velocity 20+4 24 (kmh) Reverse velocity 20-4 16 (kmh).

The least common multiple of 24 and 6 is 48, assuming that the distance between piers A and B is 48 km. The time it takes to go is 48 24 = 2 hours, and the time to come back is 48 16 = 3 hours. It took 5 hours to travel to and from piers A and B.

But the original title was hours,. 5 times, so the actual distance between piers A and B is kilometers.