20 12 fourth grade hope cup 100 question

1. Known (1+1+) × 37 =11,

(2+2+2)×37=222,

(3+3+3)×37=333,

Then 24× 37 = _ _ _ _ _ _.

2. In a division formula, the dividend is 173 and the divisor is a natural number and equal to the quotient, so the sum of the remainder, divisor and quotient is _ _ _ _ _ _ _ _.

3. Define operations "▽" and "△": When a≥b, a ▽ b = b ▽ a = b, a △ b = b △ a = a ... If the zero natural number m is not satisfied,

5 △ 7 △ (m △ 4) = 6, then m = _ _ _ _ _ _ _

As we all know, the product of three natural numbers is odd. If the product of two of these three numbers minus 1 is 4 16, then the product of the original three numbers is _ _ _ _ _.

5. The last digit of the formula1× 3× 5× 7× 911is _ _ _ _ _.

6. If the product of six consecutive odd numbers is 135 135, then the sum of these six numbers is _ _ _ _ _ _.

7. If the area of each small square in the figure 1 is 1, then the area of the shadow quadrilateral ABCD is _ _ _ _ _ _ _.

8. If five 3s are multiplied to get a, 20 1 1 5 is multiplied to get b, and 20 12 is multiplied to get c, then the result of a×b×c is _ _ _ _ _ digits.

9. Twenty-eight children line up, counting from left to right, with 10 being Zhang Hua and Li Ming on Zhang Hua's left. Then counting from right to left, Li Ming is _ _ _ _ _ _.

10. The continuous natural numbers 1, 2, 3, 4, 5, 6, 7, ... are one after another, and the result is 20 12. When checking, it was found that a number was missing, so the missing number was _ _ _ _ _ _ _ _.

1 1. There are some red beans and mung beans on the table, and the number of mung beans is 1 1 times that of red beans. Later, mung beans began to sauvignon blanc, and 45 of them turned into red beans. At this time, there are as many red beans as mung beans, so there are already _ _ _ _ _.

12. Divide 120 boys and 140 girls into several groups. If each group has the same number of boys and girls, it can be divided into _ _ _ _ _ _ _ _ groups at most.

13. If 2011= □ 4 □□ □17, there are _ _ _ _ _ formulas that meet the requirements.

The nine numbers 14. 1, 2, 3, 4, 5, 6, 7, 8 and 9 constitute the formula shown in Figure 2 (each number only appears once). Four numbers have been given. Please fill in the appropriate numbers in the box.

15. A rectangular cardboard is 70 cm long. After cutting off the largest square, there is a small piece of rectangular cardboard left. Make a photo frame with this rectangular cardboard, and the circumference of the photo frame is _ _ _ _ _ _ _ _ _ _ cm.

16. If it is divisible by 1 1, then the minimum value of n is _ _ _ _ _ _.

17. There are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

18. If a-b=303 and A ÷ B = 26...3, then A+B = _ _ _ _ _ _ _ _ _ _ _ _ _

19. The age of the four children is four consecutive even numbers, and their average age is seven years old, so the oldest is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

20. In a math exam, the scores of A, B, C and D are different integers with an average of 95 points. Among them, D gets the perfect score of 100, and the scores of B and C are higher than the average, so the highest score of A is _ _ _ _ _ _.

2 1. It is known that the sum of two numbers is 73, and the larger number is divided by one bit to get the smaller number, so the product of these two numbers is _ _ _ _ _ _ _ _.

22. Several students are standing in a square with 20 rows and 20 columns. Now if you remove five rows and five columns, you will lose _ _ _ _ _ _ _ individuals.

23. Three digits are divisible by three. After removing its single digits, the two digits are multiples of 17. Among the three digits that meet the requirements, the largest is _ _ _ _ _ _ _.

24. There is a list of formulas:

1+2+3=6,

3+5+7= 15,

5+8+ 1 1=24,

7+ 1 1+ 15=33,

……

Then, the third expression with an addend of 8027 is the _ _ _ _ _ _ _ th expression from top to bottom. Please write this expression: _ _ _ _ _ _.

25. If the sum of two digits is 79, then the maximum value of a×b×c×d is _ _ _ _.

26. Match a three-digit number with 2 1. If you remove two matches from each "",you can get another three-digit number. Of all the three possible numbers, the largest is _ _ _ _ _ _ _ _, and the smallest is _ _ _ _ _.

27. A monkey ate 63 peaches, ate half and half on the first day, and then ate the remaining half and half the day before, so the peaches were eaten after _ _ _ _ _ _.

28. It is stipulated that when (k is a constant),

Known:.

29.2, 5, 5, 6, 6 and 9 can form _ _ _ _ different six digits, where _ _ _ _ _ _ is a multiple of 5.

30. A school offers elective courses, including three courses in humanities and social sciences and four courses in literature and art, among which Li Ming has to take three courses. If you are required to choose at least one of these two courses, there are _ _ _ _ different ways to choose.

3 1. In the formula shown in Figure 3, different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers. Then "ao" means the number _ _ _ _, "number" means the number _ _ _, and "good" means the number _ _ _ _ _.

32. There are 8 orchards along the way, and the difference between apple trees in any two adjacent orchards is 1. Can the total number of apple trees in these eight orchards be 22 1? Why?

Can all squares in the grid table of 33.9× 100 be filled with a non-zero natural number, so that the sum of the numbers filled in each row and the sum of the numbers filled in each column are prime numbers? Why?

34. The bus stop sign of a bus line says "binary 12, 5, 5", that is, you charge two yuan when you get on the bus, and you can take 12 km. After exceeding 12 km, 50 cents will be charged for each additional 5 km. If A and B, which are 32 kilometers apart, are on this line, then the fare from A to B should be _ _ _ _ _ _ _ _ yuan.

35. Make a big rectangle with 24 small black or white squares. It is known that the outer circles of rectangles are all black squares, so there are at least _ _ _ _ _ _ _.

36. Party A, Party B and Party C plant trees in Party A and Party B, with 900 trees in Party A and 0/250 trees in Party B/KLOC ... It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees each day. Party A planted trees in Site A, Party C planted trees in Site B, and Party B planted trees in Site A first, and then went to Site B. Both plots started and ended at the same time, so B has been planted in Site A for _ _ _ _ _ days.

37. There are three line segments with lengths of 5, 7 and 9, which are respectively used as the upper bottom, lower bottom and height of the right-angled trapezoid, so the maximum area of the trapezoid is _ _ _ _ _.

38. Cut the largest square from the rectangle, and then cut the largest square. The sides of the rectangle are 5 cm and 3 cm respectively. The original rectangular area is _ _ _ _ _ cm2.

39. If a number is divided by 5, the remainder is 3; if it is divided by 4, the remainder is 1. If this number is divided by 20, the remainder is _ _ _ _ _ _ _.

40. Figure 4 is a map of two communities, and the line segments are streets. From the upper left A to the lower right B, each intersection can only go straight or turn right, so * * * has _ _ _ different routes.

The 4 1. bus uses the 2 1 subcomponent to display line numbers. If one of the display parts is turned off and the route is displayed incorrectly, the original route may be _ _ _ _ _ _ _.

42. Four children want to buy movie tickets for four adjacent seats in the last row. If there are 26 seats in the last row and the seats from 8 to 19 have been sold, they have _ _ _ _ ways to buy tickets for this row.

43. Divide a non-zero natural number by the sum of several non-zero natural numbers, and then find the products of these divisors respectively. Knowing that the maximum product is 36, the original number is _ _ _ _ _ _ _ _.

44.a and B take turns taking candy from the package. A takes 1 block, and B takes 2 blocks; Then a takes 3 pieces and b takes 4 pieces; ……; And so on. If anyone meets less candy in the bag this time than he should, he will take all the candy left in the bag. If a * * * takes 10 1 candy, there are _ _ _ _ candy in the bag at the beginning.

45. In the 30-meter-long and 20-meter-wide open space, if the specified row spacing and column spacing are 5 meters, at most _ _ _ _ trees can be planted.

46. As shown in Figure 5, the side length of the square ABCD is 4cm, and the intersection of diagonal lines is O. When the right angle △EOF rotates around the O point, the area of the male * * * part (shadow part) of the square ABCD and △ EOF remains unchanged, and the area of the shadow part is _ _ _ _ cm2.

47. There is a square forest (as shown in Figure 6). Its side length is1000m. There are pine and cypress trees here. Uncle Li walked into the forest from the southwest corner of the square and began to walk due north. When he met a pine tree, he walked due east. When he met a cypress tree, he walked to the north.

48. Fill the odd numbers 1, 3, 5, 7 and 9 in the following boxes respectively, so that the equation holds:

□×□□×□□=2223.

(Note: 1 □ stands for one digit, and 2 □ (i.e. □□) stands for two digits. )

49. An internal angle of an isosceles triangle is 50, so the degree difference between this internal angle and the maximum angle and minimum angle of this triangle is _ _ _ _ _ _.

50. For a arithmetic progression, the sum of 1, 5 and 9 is 1 17, 3 and 7 and the sum of 1 1 is1,so this arithmetic progression is the first.

(Note: If the number in a column starts from the second item, and the difference between each item and its previous item is equal to the same number, this series is called arithmetic progression. )

5 1. There are enough balls of 10 colors in the vending machine. Xiaoming wants to buy a pair of balls of the same color. If the unit price of the ball is 2 yuan, then, in order to ensure that Xiao Ming realizes his wish, he must spend at least _ _ _ _ _ _ _ yuan.

52. Put the four numbers 1, 2, 3 and 4 on the four vertices of a square at will, and multiply the numbers on every two adjacent vertices to get four products. Then the minimum value of the sum of these four products is _ _ _ _ _ _ _ _, and the maximum value is _ _ _ _ _ _ _.

53. A group of rabbits are pulling radishes in the vegetable field. Two rabbits each pulled out four radishes, and the other two rabbits each pulled out five radishes. At this point, there are 12 radishes left in the field. If each rabbit pulls out six radishes, it's over. Then * * * has _ _ rabbits instead of _ _ radishes.

54. When Ma Xiaohu counted the average score of a group exam, he mistyped Li Ming's 96 points as 69 points, and the calculated average score was 87 points. After the discovery, she revised the average score to 90, so there are _ _ _ _ students in this group.

55. Five contestants, A, B, C, D and E, took part in the math contest. After the game, the staff introduced the results of the game in six sentences:

(1)A comes second, and B comes third.

(2)E is 1 and C is the fifth.

(3) Row D 1, and row C is the second.

(4)A is the second and E is the fourth.

(5)B is 4 and D is 5.

If the above five sentences are half right and half wrong, then the rankings of the five players A, B, C, D and E are _ _ _ _.

56. Fill in the seven numbers 1 2.

57. As shown in Figure 8, according to the law given in the figure below, the seventh number consists of _ _ _ _ _ _ "○".

Xiao Cong wants to plant colorful flags around the playground, as shown in Figure 9. If a flag is inserted every 5 meters, Xiao Cong needs to insert a colorful flag _ _ _ _ _.

59. As shown in figure 10, the four vertices of the square EFGH are the midpoints of the sides of the quadrilateral ABCD. Known delta △AEH,

The areas of △CFG are 12 cm2 and 10 cm2 respectively, so the area of quadrilateral ABCD is _ _ _ _ _ cm2.

60. As shown in figure 1 1, fill the number 1-9 into the English letter areas in two circular rings respectively, so that the difference (large number reduction) between the numbers in any two adjacent areas (areas with common edges are called adjacent areas) is at least 2. Then three digits = _ _ _ _.

6 1. As shown in figure 12, fill in 0-9 in the ellipse, and only one number can be filled in each area, and all numbers will not appear repeatedly. Numbers in two areas with common edges cannot be adjacent natural numbers. Then = _ _ _ _ _ _. (Note: 0 and 1 are adjacent natural numbers, and 0 and 9 are not adjacent natural numbers. )

62. An express train and a local train run in opposite directions on two parallel tracks. The express train is 420 meters long and the local train is 525 meters long. The time for people sitting on the express train to see the local train pass is 15 seconds, so the time for people sitting on the local train to see the express train pass is _ _ _ _ _ _ _.

63. The Bureau of Landscape Architecture plans to pave a rectangular field with two different shades of grass, with the dark grass forming a letter pattern and the light grass as the background. If it is T-shaped, dark grass accounts for 35 square meters; If it is shaped like an "F", dark grass occupies 50 square meters. Assuming that the letters are in the same direction, the width of the grass belt is the same, and each stroke reaches the maximum, then the area occupied by the dark grass when forming the "E" shape is _ _ _ _ square meters.

64. Shooting training regulations: when a rifle fires 10 bullets, two bullets will be awarded for each hit of the bull's-eye; Shoot with a pistol, shoot 14 bullets, and reward 3 bullets for each hit. Miss Wang shoots with a rifle, while Miss Li shoots with a pistol. When they have distributed all the bullets and won the prize, they shoot evenly. Miss Wang hit the bull's-eye 20 times and Miss Li hit the bull's-eye _ _ _.

65. It is known that six people A, B, C, D, E and F watched 5, 5, 6, 8, 8 and 10 performances respectively. The unit price of an adult ticket is twice that of a child ticket. Known fares are all integer yuan, and the ticket cost is 1026 yuan, so the unit price of adult tickets is _ _.

66. Every blank square in figure 13 is a square with equal sides, and the width of the shaded part is equal. The shaded area is _ _ _ _ _ _ _ square centimeters.

67. Choose 1 student from 20 outstanding students to participate in international exchange activities. The selection method is that 20 students stand in a row, count off, odd students are unsuccessful, and the queue is launched. The rest of the students reported in turn, and the odd students still lost the election and launched the queue. Xiaoming really wants to take part in this activity. In order to ensure that he is selected, the number of times he queues for the first time should be _ _ _ _ _.

68. Figure 14 is the flower shop plant pattern, with the first circle (length 7) from O to A7 and the second circle from A7 to A20. If OA1= oa2 = a1a2 = a2a3 = a3a4 = a4a5 = ... = 65438+.

69. Figure 15 is a graph composed of circles. If it continues to change according to the given law, there are _ _ _ _ cycles from top to bottom 10 layer.

70. As shown in figure 16, p is any point on the diagonal BD of rectangular ABCD, which is used to train PA and PC. Please explain the relationship between the area of △ADP and the area of △CDP, and explain the reasons.

7 1. Xiao Fang lives on the 7th floor of Yue Ming Building, and the floor spacing between every two floors of the building is 17 steps. Xiaohong's house is downstairs in Xiao Fang's house. Xiao Fang can walk down 85 steps from home to Xiaohong's house, so Xiaohong lives on the _ _ _ _ _ floor.

72. If the average number of prime numbers in 15 is m, the sum of all possible values of m is _ _ _ _ _.

74. Legend has it that in the Xia Dynasty, a turtle appeared in Luohe, and there was a picture on its back, which was later called "Luo Shu". "Luo Shu" is to fill in nine numbers 1 to 9 in nine squares as shown in figure 17, so that the sum of numbers on each row, column and two diagonal lines is equal. If the middle number 5 is changed to 6, please fill in the situation that the sum of the numbers in each row and column is equal in Figure 18.

75. Put a square ABCD with a side length of 6 cm and an isosceles right triangle AFE with a hypotenuse length of 8 cm together, as shown in figure 19. Then the area of the shadow quadrilateral AFGB in the figure is _ _ _ _ _ _ square centimeters.

76. As shown in Figure 20, two squares ABCD and BEFG with side lengths of 8 cm and 6 cm respectively are arranged side by side, and the G point is on the BC line, then the area of the shadow quadrilateral ABFG is _ _ _ _ square cm.

77. Make an equilateral triangle with 30 sticks of equal length, as shown in Figure 2 1. There are _ _ _ _ equilateral triangles in the picture.

78. Count it, there are _ _ _ _ triangles in Figure 22.

79. Figure 23 is a graph composed of five squares with the same size (the midpoint of a group of adjacent sides of the left square coincides with the midpoint of a group of adjacent sides of the right square). The circumference of this figure is 96 cm. Then its total area is _ _ _ _ square centimeters.

80. Annie has five chocolates. She should eat at least one every day and eat the whole piece until she finishes eating. * * * There are _ _ ways to eat.

8 1. Figure 24 is an expansion diagram of a cube 1 1 and two camouflage diagrams (not the expansion diagram of a cube). Please point out which two camouflage pictures?

82. It took 32 minutes to make a kite in Workshop A last year, and you can make 15 kites every day. This year, the workshop has improved the technology, and the time for making each kite has been reduced by 8 minutes compared with last year, so Workshop A can make _ _ _ _ _ _ _ kites a day this year.

83. The top angle of an isosceles triangle is 50, and two right triangles are obtained by folding in half along the height of a waist. The difference between the degrees of the two larger acute angles in these two right triangles is _ _ _ _ _ _ _.

84. As shown in Figure 25, if the side length of square ABCD is 3, square AEFG becomes 4, S 1=S2, S3=S4, then the area of square DEHK is _ _ _ _ _.

85. Design a flower bed with an equilateral triangle from the inner layer to the outer layer. As shown in Figure 26, there is 1 potted flower at each point. If the flower bed has 10 layer, then * * * should use _ _ _ _ potted flowers.

86. With the nine numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9, can we form the smallest nine digits divisible by 1 1? If you can, please write this nine-digit number and write the thinking process; If not, please explain why.

87. In the result of 2× 4× 5× 8×16× 25×125× 625×11025, the number "0" * * * appeared _ _ times.

88. As shown in Figure 27, the side length of square ABCD is 4cm, BD is diagonal, and the midpoints of BC and CD are E and F respectively, connecting EF, the midpoint of EF is I, the intersection of AI and BD is G, and the midpoints of BG and DG are H and J respectively, connecting e H and IJ, and using A, B, C, D, E and X respectively.

According to the area, these seven numbers can be divided into three or four groups, so that the sum of the areas of each group is equal? If not, please explain the reasons; If yes, please write down the grouping situation.

89. Fill in other numbers from 1 to 16 in the blank space in Figure 28, so that the sum of numbers in each row, column and diagonal is equal.

90. Pool A and Pool B are known to have 69 tons and 36 tons of water respectively. If the water in pool A flows into pool B at a rate of 2 tons per minute, the water in pool B is twice as much as that in pool A after _ _ _ _ minutes.

9 1, the mother squirrel and the little squirrel each have a box of pine nuts. There are twice as many pine nuts in mother's box as in little squirrel's box. If mother squirrel eats 5 pine nuts every day and little squirrel eats 3 pine nuts every day, then when little squirrel eats all the pine nuts, mother has 20 pine nuts left. Q: How many pine nuts did Mother Squirrel and Little Squirrel have at first?

92. As shown in Figure 29, in the rectangular ABCD, EF∨AD, GH∨AB, EF and GH intersect at point O, and the area of rectangular OFCH is 6 square centimeters larger than that of rectangular AEOG. Find the area of triangle OBD.

93. As shown in Figure 30, the area of the shaded part in a 3cm× 3cm square is _ _ _ cm2.

94. Party A and Party B set out from AB and walked towards each other at the same time. An hour later, they met for the first time at a distance of 5 kilometers, and continued to move forward at the original speed after meeting. A will return immediately after arriving in B and B As a result, they met again at a distance of B 3 kilometers. Q: What is the distance between AB and B? How many kilometers per hour are Party A and Party B?

95. Mother gave Lily a big box of chocolates. Lily plans to eat an average of 35 chocolates a week so that she can finish it in four weeks. But Lily actually eats 1 chocolate less than planned every day. How many days can she finish this box of chocolates?

96. As shown in Figure 3 1, 1, 2, 3, …, 12, holes are evenly represented on a disk. A bug jumps clockwise from 1 hole, and the number of steps it jumps is specified as the number of holes it jumps. For example, jump from 1 hole to the first time. Take off m times from the x hole and jump x steps. If a bug starts from 1 hole and jumps 100 times to N(N= 1, 2,3, … 12) hole according to this rule, how many steps does it * * * jump? What is n?

97. An ant starts from point B in Figure 32 and crawls counterclockwise to point A along the graphic frame at a speed of 2 cm/s. If the ant is regarded as point M, it is connected with AB to form a triangle ABM, and the area of △ABM varies with the crawling time of the ant (Figure 33). If the area of △ABM is the largest within 8 seconds, please complete Figure 33.

98. The local train and the express train leave relatively from AB. If the local train starts two hours earlier, the local train will exceed the midpoint of 48 kilometers when the two cars meet. If the express train leaves 2 hours in advance, when the two cars meet, the express train will exceed the midpoint 144 km. If two cars leave at the same time and meet in six hours, how many kilometers is the express faster than the local train per hour?

99. A staircase * * * has 10 steps, and Xiao Wang Can takes two steps at a time, so how many ways can Xiao Wang climb the fifth step * *?

100. As shown in Figure 34, the electronic digital clock indicates the time from 00:00:00 to 23:59:59. So, how many seconds does it take to display four numbers "3" on this clock day and night?