Since primary school, we have been exposed to the Olympiad. Students' thinking and logic can be exercised through Olympic Mathematics. Below I bring you some information, hoping to help you!

one

5 1. A piece of paper is torn into 4 pieces for the first time, and then one piece is taken from the paper at a time and torn into 4 pieces, so it is torn 10 times, and * * * has _ _ _ pieces of paper.

Answer: Every time a piece of paper is torn, four sheets are produced, and one sheet is reduced, that is, three sheets are produced, and * * * has 30 sheets. Together with the original, * * * has 3 1 sheet.

52. Divide the picture below into four figures with the same shape and size, so that each figure contains a little monkey. Can you do it?

Answer: just cut it into an L shape, the answer is not unique.

53.△ + □ = 9; △ + △ + □ + □ + □ = 25; △ = *** *** ; □ = *** ***

A: Because △+□ = 9, we can change △+□ = 25 into 9, which becomes 9+△+□ = 25; Replace it again and it becomes 9+9+□=25, and it can be concluded that □ = 7; According to △+□=9 and □=7, we can get △=2.

54. In the following formula, what numbers do □, ○, △, * represent respectively? *** 1***□+5= 13-6; ***2***28-○= 15+7; ***3***3×△=54; ***4***÷3=87; ***5***56÷*=7。

Answer: * * *1* * According to the addition rules, □ =13-6-5 = 2; * * * 2 * * According to the rules of subtraction operation, ○ = 28-* * *15+7 * * = 6; * * * 3 * * According to the multiplication rule, △ = 54 ÷ 3 =18; ***4*** According to the division operation rules, = 87× 3 = 261; ***5*** According to the division operation rules, *=56÷7=8.

55. 1. Giraffe asked Lamb,' How many heads does a bamboo pole have, two bamboo poles have four heads, and four and a half bamboo poles have?' The lamb turned nine heads happily. Did the lamb answer correctly? Why?

Answer: Lamb's answer is incorrect, because even a half bamboo pole has two heads, so four and a half bamboo poles have 10 heads.

56.□+□+□+□+□=30 Fill in five consecutive natural numbers in the above □ to make the equation hold.

Answer: 4+5+6+7+8=30.

57. Observe the following numbers in order and replace them with "?" Fill in the appropriate graphics.

Answer: Add three dots one by one on each picture, in the order of adding three solid dots and three hollow dots.

58. Two mothers gave their two daughters some money, one for their daughter 120 yuan and the other for their daughter 100 yuan. When the two daughters counted their own money, the total was only 120 yuan. Children, do you know why there is only 120 yuan instead of 220 yuan?

Answer: Because there are only three people, grandmother, mother and daughter.

59. Add 5, multiply 5, subtract 5 and divide 5 to a certain number, and the result is 5. Find this number.

Answer: Push from back to front, it turns out to be addition, and push back is subtraction; It turned out to be subtraction, and pushing it back is addition; It turned out to be multiplication, and pushing back is division; It turned out to be division, and pushing back is multiplication. From the last step, "Divide by 5, the result is equal to 5" and the dividend can be calculated as 5× 5 = 30; Look at the penultimate step, "subtract 5" to get 25, and you can get the minuend 25+5 = 30; Then look at the penultimate step, "multiply by 5" to get 30, and you can get the multiplicand 30 ÷ 5 = 6; Finally, look at the step 1, "a certain number plus 5" gets 6, and a certain number is 6-5= 1. 5× 5 = 25 25+5 = 30 30 ÷ 5 = 66-5 = 1 The number of answers is1.

60. According to the law of numbers in the figure, fill in the appropriate numbers in the top blank.

Answer: 64, each number is the sum of the following two numbers.

6 1. The product of two integers is 144, and the difference is 10. Find these two numbers.

Answer: List all kinds of situations in which the product of two numbers is 144, and then find a pair that meets the conditions of the topic. 123468912144724836 241812 display difference12.

62. Xiaoming's dog drinks water regularly. He drinks water every five minutes. He drank water for the first time at eight o'clock sharp. When did the puppy drink water for the 20th time?

Answer: There are 20-1=19 * * intervals between the 20th and 60th drinking. Because the puppy drinks every 5 minutes, the interval between the 20th and 20th drinking is 19×5=95*** minutes *.

63. 100 The monk divided it into 100 steamed buns, the big monk divided it into 3 steamed buns, and the little monk divided it into/kloc-0 steamed buns, which just ended. How many people are there in the big monk and the little monk?

Answer: If there are 33 big monks, they are divided into 3×33=99 steamed buns, and the remaining 100-99= 1*** steamed buns are distributed to three small monks, so the total number of monks is 33+3=36, which is inconsistent with the known 100 monks. The number of big monks has decreased. If there are 30 big monks, divide them into 3×30=90 steamed buns, and the remaining 10 steamed buns can be distributed to 3× 10 = 30 small monks, then the total number of monks is 30+30=60. The number of big monks must also be reduced. If there are 25 big monks, divide them into 3× 25.

64. A picture book is *** 100 pages. In typesetting, only one number can be arranged in a font. Please calculate how many fonts are used in the page numbers of this book.

A: From page 1 to page 9, * * 9, each page uses 1 type, * * uses1× 9 = 9 * * *; From page 10 to page 99, * * 90 pages, each page uses 2 types, * * uses 2× 90 =180 * * * *; On page 100, only three types are used on page 1 * *, so the total number of types used on page 100 is 9+180+3 =192 * * *.

65. A piece of chalk has two heads. How many heads do three and a half pieces of chalk have?

Answer: 2x4=8 pieces of 8 chalk with 3 and a half pieces.

66. When Xiao Mahu did the addition problem, he took 3 in the unit as 5 and 8 in the tenth as 3. The total result is 2 15, and the correct answer is * * * * *.

Answer: The correct result should be 2 15-2+50=263.

67. Find out the rules and fill in the appropriate numbers in the blanks.

Answer: This question can be filled in many ways, from largest to smallest, or from smallest to largest. The difference between two numbers can be 1 or 2.3.4 or 5.

two

68. It takes 4 minutes to bake a cake, 2 minutes on each side. A pot can only bake two cakes at the same time. How many minutes does it take to bake three cakes?

Answer: A cake and B cake are put into the pot at the same time. After baking one side in 2 minutes, take out a cake and put it in the C cake. At the same time, turn the B cake over and bake for another 2 minutes. At this time, the B cake is cooked. Take out the pan and put in the A cake to bake the remaining side. At the same time, the C cake is turned over and baked together for another 2 minutes.

69. The product of two integers is 144, and the difference is 10. Find these two numbers.

Answer: list all kinds of situations in which the product of two numbers is 144, and then find a pair that meets the conditions of the topic. It can be seen that the two numbers with a difference of 10 are 8 and 18, and this pair of numbers is what you want.

There are two ropes. The first rope is 4 meters more than the second rope and 6 meters less than the third rope. How long are these two ropes?

Answer: B 10 *** meter * * A 24 *** meter * * *

7 1.5 people go to the tap to receive water, and the time to fill the tap with water bottles is 5 minutes, 3 minutes, 4 minutes, 2 minutes and 1 minute respectively. There is only one tap available now. How to arrange the water order of these five people to minimize their total waiting time? What is the shortest time?

Answer: You can draw water in the order of 1 minute, 2 minutes, 3 minutes, 4 minutes and 5 minutes, so that the sum of each person's queuing time is the smallest, and the minimum value is1× 5+2× 4+3× 3+4× 2+5×1= 35.

72. In the morning, my mother made pancakes for Xiaoming with a pan. You can put two cakes in the pot at a time. It takes 2 minutes to make 1 cake, and 1 minute for the head and tail. * * * How many minutes does it take mom to fry five cakes? How about frying six cakes?

Answer: Five cakes are two more cakes than three cakes. These two extra cakes need two minutes, of which 65,438+000% use a pan, so it takes at least 3+2=5*** * minutes * *. Fry six cakes and two cakes, of which 65,438+000.

73. As shown below, a dog is at point A and Xiaofeng is at point B. They are moving towards each other. Xiaofeng walks 5 meters a minute, and the dog runs 20 meters a minute. After encountering Xiaofeng, the dog ran back to point A, then ran towards Xiaofeng, and ran back to point A after encountering Xiaofeng. How many meters did Xiaofeng run in five minutes' walk? A——————————B

Answer: 20×5= 100*** meters * * *

How much is 74.368- 199?

Answer: The original formula = 368-200+1=168+1=169.

75. In a math exam, the scores of Xiaoling and Xiaojun add up to 195, Xiaoling and Xiao Fang add up to 198, and Xiaojun and Xiao Fang add up to 193. How many points did they get?

Answer: List the following equations: Xiaoling+Xiaojun = 195 * * 1 * * Xiaoling+Xiao Fang = 198 * * 2 * * Xiaojun+Xiao Fang =193 * * 3 * *. Get 2 * * * Xiao Ling+Xiao Jun+Xiao Fang * * = 586, namely Xiao Ling+Xiao Jun+Xiao Fang =293 ***4*** from ***4** formula-* *1* * formula Xiao Fang = 293-65438. *3*** Xiaoling =293- 193= 100 shows that Xiao Fang scored 98 points, Xiao Jun scored 95 points and Xiaoling 100 points.

76. Look at the picture below. How many minutes did Tong Tong spend doing his Chinese homework? How many minutes does it take to do math homework? How many hours does a * * * take?

A: From 4: 00 to 4: 40, the clock runs for 30 minutes; 10 From 4: 40 to 5: 00, the clock runs for 30 minutes. The clock runs for 30 minutes +30 minutes =60 minutes +60 minutes = 1 hour. Chinese homework and math homework take 30 minutes. It takes 1 hour to do math homework.

77. As shown in the figure below, it is a tower composed of small cubes. Please count, how many pieces are there in * * *?

Answer: From top to bottom, the first floor is1; 4 blocks on the second floor; 9 blocks on the third floor; The fourth floor/KLOC-Block 0/6; Total 1+4+9+ 16=30*** blocks * *.

78. A bus with 78 seats is empty. First stop 1 person, second stop 2 people, third stop 3 people. If this situation continues, how many stops will the bus be crowded with passengers?

Answer: * * *1+12 * *12 = 7812 station, the bus is full of passengers.

79.M * N = * * * M+N * * * * 2，* * * 2008 * 20 10 * * * * 2009 = _ _ _ _ _ _ _ _ _ _ _ _ _ .

A: According to the new calculation, 2008 * 2010 = * * 2008+2010 * * ÷ 2 = 2009. 2009*2009=***2009+2009***÷2=2009。

80. Today is Tuesday. What day is 50 days later?

Answer: Every 7 days, 50=7x7+ 1, and the remainder is 1, so add 1 on Tuesday. So it's Wednesday in 50 days.

8 1. Look at the picture below and fill in the appropriate numbers in the blanks.

Answer:

82. Xiao Ming has three numbers in his mind, and the sum of these three numbers is equal to the product of these three numbers. Do you know what the three numbers that Xiao Ming thinks of are?

Answer: Three numbers are 1, 2, 3. Test 1+2+3=6 1×2×3=6, so 1+2+3= 1×2×3.

83. There is a pile of candy on the table. Two mothers and two daughters, a grandmother and a granddaughter each took a piece. This pile of candy is finished, and there are only three pieces in this pile. Why?

Answer: Because there are only three people, grandma, mom and girl.

84. In the final exam, Xiaoming scored an average of 89 in politics, Chinese, mathematics and English, 9 1.5 in politics and mathematics, 84 in Chinese and 86 in political English, and English was more than Chinese 10.

Answer: ① English * * * 84× 2+10 * * * ÷ 2 = 89 * * * ② Language 89-10 = 79 * * * ③ Politics 86× 2-89 = 83 * *.

three

85. Cutting a 90-meter-long red rope into three sections requires that the second section is 3 meters more than the first section, and the third section is 3 meters more than the second section. How should I cut it?

Answer: 27,30,33 The length of the second root is 90 ÷ 3 = 30m, the length of the first root is 30-3 = 27m, and the length of the third root is 30+3 = 33m.

How many different four-digit numbers can the four numbers 86.2, 5, 0 and 7 make up?

A: The enumeration methods that can be used are 2057, 2075, 2507, 2570, 2750, 2705, 3027, 3072, 3207, 3270, 3702, 3720, 7025, 7052, 7205, 7250, 7502.

87. Mom and Dad took their son, daughter and a dog on a trip. On the way, they must cross a river. There is an empty boat at the ferry, which can carry 50 kilograms at most, while 50 kilograms for mom and dad, 25 kilograms for son and daughter, and 0 kilograms for dog/kloc-0. How can they all cross the river?

Answer: The carrying capacity of the ship is 50 kilograms, so mom and dad can only cross the river alone. Son and daughter can cross the river at the same time; Son * * * or daughter * * * can take the dog across the river, except that the boat has to be rowed back. The son and daughter crossed the river for the first time, and the son * * * or daughter * * * rowed the boat back; The second time my father * * * or mother * * * crossed the river, my daughter * * * or my son * * * rowed the boat back; The son and daughter crossed the river for the third time, and the son * * * or daughter * * * rowed the boat back; The fourth time mother * * * or father * * * crossed the river, daughter * * * or son * * * rowed the boat back; The fifth time the son * * * or daughter * * * crossed the river, the son * * * or daughter * * * rowed the boat back; My son and daughter crossed the river for the sixth time. So the whole family crossed the river.

88.8 1 Students perform gymnastics in 9 rows and 9 columns. Xiaohong is in the square, with two students on the right and three students in front. At this time, the whole phalanx turned right, so Xiaohong had * * * * students in front and * * * students on the right.

Answer: Xiaohong has two students on her right and three students in front, so she has 9- 1-2=6 students on her right and 9- 1-3=5 students on her right. If the students in the whole phalanx turn right, Xiaohong has six students on his right and five students on his right.

89. In the following formula, what numbers do □, ○, △, * represent respectively?

*** 1***□+5= 13-6;

***2***28-○= 15+7;

***3***3×△=54;

***4***÷3=87;

***5***56÷*=7。

Answer: * * *1* * According to the addition rules, □ =13-6-5 = 2; * * * 2 * * According to the rules of subtraction operation, ○ = 28-* * *15+7 * * = 6; * * * 3 * * According to the multiplication rule, △ = 54 ÷ 3 =18; ***4*** According to the division operation rules, = 87× 3 = 261; ***5*** According to the division operation rules, *=56÷7=8.

90. There are two kettles, one can hold 500 grams of water and the other can hold 300 grams of water. Can you weigh 400 grams of water with these two kettles?

Answer: First, fill a 500g kettle with water, pour it into a 300g kettle, then empty the second kettle, pour the remaining 200g water from the first kettle into the second kettle, then fill the first kettle with 500g water, and pour 100g into the second kettle. The second pot is exactly 300g water, and the first pot is 400g water.

9 1. Look at the picture below. How many minutes does it take Tong Tong to do his Chinese homework? How many minutes does it take to do math homework? How many hours does a * * * take?

A: From 4: 00 to 4: 40, the clock runs for 30 minutes; 10 From 4: 40 to 5: 00, the clock runs for 30 minutes. The clock runs for 30 minutes +30 minutes =60 minutes +60 minutes = 1 hour. Chinese homework and math homework take 30 minutes. It takes 1 hour to do math homework.

92. Find out the rules and fill in the appropriate numbers in the blanks.

Answer: Among the three small triangles around the first triangle, the sum of the three numbers in 2.3.5 is equal to the number in the middle triangle, which is 10. It can be seen that the sum of the numbers in the three small triangles around each triangle is the number in the middle triangle, that is, 10, that is, the number in the middle triangle continuously subtracts the two around it. According to this rule, the number in the third triangle is 10- 1-4=5, and in the fourth triangle, the number in the small triangle above is 10-7-3=0.

93. Bottled soda factory stipulates that every three empty bottles can be replaced with 1 bottle of soda. Mom bought six bottles of soda for Xiaoming, so that she can drink * * * * * bottles of soda as soon as she * * *.

Answer: 6÷3=2*** *, Xiaoming can change 2 bottles first, and then he has 2 bottles, so he can change another bottle. After drinking, just three bottles are returned to the store, and he can drink 6+2+ 1=9*** *.

94. The robot cat made a magic alarm clock, which rang several times every hour and several times every half hour. When the robot cat began to watch Pleasant Goat and Big Big Wolf, it heard the alarm clock ring twice. When he finished reading, the alarm clock just rang again. While watching cartoons, he heard the alarm clock go off 12. So when did he finish watching this cartoon?

Answer: 430

95.3 boxes of apples weigh 45 kilograms. A box of pears is 5 kilograms heavier than a box of apples. How much do three boxes of pears weigh?

Answer: You can first find out that the weight of three boxes of pears is more than that of three boxes of apples, plus the weight of three boxes of apples, which is the weight of three boxes of pears. 45+5× 3 = 45+15 = 60 * * * kg * * A 3 boxes of pears weigh 60 kg.

96. Xiaoling has 46 ducks and 24 chickens, and the total number of chickens and geese is 5 more than that of ducks. How many geese does Xiaoling have?

Answer: 5 1-24=27*** Only * * *

To sum up, the total number of chickens and geese is 46+5 = 51* * and then the number of geese is 51-24 = 27 * * *.

97. Xiaojun and Xiaohao originally spent the same money on several pencils of the same kind. Later, Xiaojun took 13 pencils, Hao took 7 pencils, and Xiaojun gave Xiao Hao 3 cents. How much is each pencil?

Answer: Xiao Hao took several pencils, * * * 13-7 * * * * ÷ 2 = 3 * * * *, how much is each pencil? 3÷3= 1*** *.

98. There is a column of numbers 2,4, 1, 2,4, 1, 2,4, 1, … What is the 25th number? What is the sum of these 25 numbers?

Answer: 258

Analysis 25÷3=8.3, so the 25th number is 2.

Every third number is a period, 2+4+ 1 = 7, the 25th number contains 8 such periods, and the 25th number is 2, so the sum of these 25 numbers is 7×8+2=58.

99. A round biscuit can be cut into 1 knife, 2 knives, 3 knives and 4 knives. How many pieces can each person cut?

Answer:

100. The teacher prepared 10 pencil boxes, of which 5 have pencils, 4 have pens, and 2 have both pencils and pens. The teacher's question is how many pencil boxes are empty?

Answer: 3