Examination paper and answer of fifth grade mathematics competition

Seven odd numbers and even numbers (one)

Grade class name score

Fill in the blanks

1.2, 4, 6, 8, ... are continuous even numbers. If the sum of five consecutive even numbers is 320, the smallest of these five numbers is _ _ _ _ _.

2. There are two prime numbers whose sum is an odd number less than 100 and a multiple of 17. These two prime numbers are _ _ _ _.

3. There are 100 natural numbers whose sum is 10000. In these numbers, there are more odd numbers than even numbers, so there are at most _ _ _ even numbers in these numbers.

4. The picture on the right is a target paper, and 1, 3, 5, 7 and 9 on the target paper indicate the scores of hitting the target area. A said: I shot six times and each shot hit a target. * * * got 27 points. B said: I shot three times, each shot hit a target, and * * * got 27 points.

1 3 5 7 9

It is known that one of Party A and Party B is telling the truth, so it is _ _ _ _ _.

5. An electric mouse starts from point A in the upper right picture and runs along the grid line, turning left or right at each grid point. When the electric mouse returned to point A, A said * * * turned 8 1 time, and B said * * * turned 82 times. If one of them is right, who is right?

6. There are 20 questions in a math exam * * *, and it is stipulated that if one question is answered correctly, it will get 2 points, and if one question is answered incorrectly, it will get 1 point, and the unanswered questions will not be scored. After the exam, Xiao Ming will get 23 points in the exam. He wants to know how many questions he made wrong, but only remembers that the number of unanswered questions is even. Please help Xiao Ming do the math. He got the wrong answer.

7. There are many articles *** 15, and the page number of each article is 1, 2, 3 ... respectively 14 and 15. If these articles are bound in a certain order and numbered uniformly, the first page of each article is at most odd.

8. One page in the middle of a book has been torn off, and the sum of the remaining page numbers is 1 133. This book has _ _ _ _ _ pages, and the torn pages are _ _ _ _ _ and _ _ _ _ _.

9. There are eight boxes, and each box contains the same kind of pen. The number of pens in the eight boxes is 17, 23, 33, 36, 38, 42, 49, 5 1 respectively. Among these pens, the number of ballpoint pens is twice that of pens, and the number of pens is that of pencils.

10. A math contest prepared 35 pencils as prizes for students who won the first, second and third prizes. The original plan was to have 6 pencils for the first prize, 3 pencils for the second prize and 2 pencils for the third prize. Later, it was changed to first prize per person 13 pencils, second prize per person with 4 pencils and third prize per person 1 pencil. Then I won the second prize.

Second, answer the question.

1 1. As shown below, plant a tree every 3 meters from 0: 00. If you hang three "Care for Trees" Xiao Mu cards on three trees, at least the distance between two trees is equal (in meters). Try to explain why.

12. On the small globe, the great equatorial circle intersects with a great circle passing through the north and south poles at points A and B. Two ants, one black and one white, start from point A and crawl along these two great circles respectively. It takes 10 second for black ants to climb the great equatorial circle, and 8 seconds for termites to climb the great polar circle. Q: 10 minutes, it is black and white. Why?

13. As shown on the right, there are 9 positions on a circle, numbered as 1~9 in turn. Now there is a small ball at the position of 1. On the first day, push the position of 10 clockwise, and the position of 14 counterclockwise the next day. The odd-numbered days after that are the same as the first day.

14. Fill in a natural number (which can be the same) in each picture on the right, so that the difference between the numbers in any two adjacent pictures (the reduction of large numbers) is exactly equal to the number of tags between them. Can you do that? Why?

———————————— Answer the case ————————

1.60

The third (middle) even number of these five consecutive even numbers is 320 5 = 64. So the smallest even number is 60.

2.2,83

Because the sum of two prime numbers is odd, one of them must be 2. The odd multiples of 17 less than 100 are 17, 5 1 and 85, and the difference between 17 and 5 1 and 2 is not a prime number, so the other prime number is 85-.

3.48

Because the sum of1000 natural numbers is 10000, that is to say, there must be even and odd numbers in1000 natural numbers, and because there are more odd numbers than even numbers, there are only 48 even numbers at most.

4.A.

Because the scores are all odd numbers, and the sum of six odd numbers is even, it can't be odd number 27, so it is A who tells lies.

5.a

Because the mouse encounters a grid to turn, it turns as many times as it passes through the grid. As shown in the picture on the right, the mouse starts from the black point and turns an odd number of times when it reaches any black point, so A is correct.

6.3

Xiaoming must have made an odd number of mistakes. If he did 1, he should do 12 to get 12 2- 1=23, so Xiao Ming * * * did 13, and the number of unanswered questions was not even. If you do three wrong questions, you have to do 13 correctly to get 13 2-3=23 points, so there are four unanswered questions, which are even numbers. Besides, Xiao Ming can't make more than five mistakes. Therefore, he made three mistakes.

7. 1 1

According to the property of odd+even = odd, the articles with even pages (2 pages, 4 pages, …, 14 pages) are arranged first, so that the first pages of 7 articles in * * * are all odd pages.

Then, arrange odd articles (1 page, 3 pages, …, 15 pages). According to the property of odd number+odd number = even number, the first pages of the four articles are all odd numbers.

Therefore, the maximum number of articles with odd page numbers on the first page of each article is 7+4= 1 1.

8.48,2 1,22

Let the page number of this book be a natural number from 1 to n, and the correct sum should be

1+2+…+n= ( n+ 1)

According to the meaning of the question, (n+1) >; 1 133

According to the estimation, when n=48, (n+1) = 48 49 =1176,176-1133 = 43. Arrange the pages according to their page numbers.

9.49

According to the meaning of the question, if there are 1 pens, there are 2 ballpoint pens and 3 pencils, that is, the total number of these three pens must be a multiple of 6, that is, they can be divisible by 2 and 3 at the same time. And because the number of pens in 3 out of 8 boxes is even, and the number of pens in 5 boxes is odd, we can know that there are pencils and pencils according to even+odd = odd.

1+7+2+3+3+3+3+6+3+8+4+2+4+9+5+ 1=64

Because 64-(4+9)=5 1 is divisible by 3, there are 49 markers in the box.

10.3

First of all, according to "13 pencils are distributed to everyone who won the first prize later", it can be determined that the number of people who won the first prize is not more than 3. Otherwise, it is impossible to distribute no less than 39 pencils just for the first prize, which has exceeded 35. Secondly, consider the situation that two people won the first prize or 1 person respectively:

When two people won the first prize, the number of pencils that won the second and third prizes according to the original scheme should be 35-6 2 = 23, and the number of pencils that won the second and third prizes after the change should be 35-13 2 = 9. Because 23 is an odd number, if there are two pencils for each third prize according to the original plan, the total number of pencils for the third prize must be even. Therefore, the number of people who won the second prize must also be odd. According to the revised "four second prizes for each person", it can be determined that only 1 will win the second prize (otherwise, more than nine pencils will be distributed for the second prize alone), which is impossible after inspection, that is to say, two people will not win the first prize.

When 1 person won the first prize, the number of pencils that won the second and third prizes according to the original scheme should be 35-6=29, and the number of pencils that won the second and third prizes after the change should be 35- 13=22. Because 29 is still an odd number, similar to the discussion in the previous case, it can be determined that the number of pencils that won the second prize must be an odd number.

1 1. The distance between the farthest two re symbols is equal to the sum of the distances between them and the middle one. If the distances between three re symbols are all odd, "odd+odd = odd" will appear, which is obviously not true, so the distance between two re symbols must be even.

12. Meet 0 times. (Black and white ants can never meet at point B)

It takes five seconds for black ants to climb a semicircle and four seconds for termites to climb a semicircle. Black ants and white ants start from point A at the same time. To meet at point B, two conditions must be met: ① Black ants and white ants have the same crawling time; ② During this time, the two ants crawl an odd number of semicircles. It takes odd seconds (5 odd) for black ants to climb odd semicircles, and even seconds (4 odd) for termites to climb odd semicircles. Odd and even cannot be equal.

13. clockwise forward 10 bit, which is equivalent to clockwise forward 1 bit; Counterclockwise advancing 14 bit is equivalent to clockwise advancing 18- 14=4 (bit), so the original title is equivalent to: advancing 1 bit clockwise every day, and advancing 4 bits alternately until the number of advancing bits is a multiple of 9.

Number of positions promoted by rotation on even days:

5, 10, 15,20,25,30,35,40,……

Number of positions rising continuously on odd days:

1,6, 1 1, 16,2 1,26,3 1,36 ,4 1,……

I entered 36 positions before 15, and 36 days is a multiple of 9, so I returned to 1 position on 15.

14. No.

If you can, let the top number be odd (see the figure below), which is made up of

Odd odd number = even number;

Even even number = even number;

Odd even number = odd number,

Clockwise inference, the middle of the top should be even and contradictory.

The same is true when the top is even.