What is the sum of all natural numbers of 1? With 100/to 1 00? 2. Goldbach conjectures that "any even number not less than 4 can be expressed as the sum of two prime numbers".

Q: 168 is the sum of two prime numbers, one of which is a single digit 1. 3. Divide 2 1, 26, 65, 99, 10, 35, 18, 77 into several groups, and ask any two numbers in each group to be prime numbers, at least how many groups should they be divided into? How to divide it? The product of three prime numbers is exactly 7 times their sum. Find these three prime numbers.

5. The sum of two natural numbers is 72, and the sum of their greatest common divisor and least common multiple is 2 16. What are these two numbers? 6. A seven-digit1993 □□□□□ can be divisible by 2, 3, 4, 5, 6, 7, 8 and 9 at the same time, so what are its last three digits in turn? 7. The sum of eight consecutive natural numbers is not only a multiple of 9, but also a multiple of 1 1. What is the largest and smallest of these eight natural numbers? 8. Write 10 consecutive natural numbers, all of which are composite numbers. 9. 1! +2! +3! +…99! What are the last two digits of? (note: n! = 1 * 2 * 3 * ...* n) 10。 There are 200 colored light bulbs hanging in the amusement hall of Children's Palace. These light bulbs are either bright or dark, which is very interesting.

These 200 bulbs are numbered according to 1~200, and their light and shade rules are as follows: in the first second, all bulbs are on; In the second second, every light bulb numbered as a multiple of 2 changes from bright to dark; In the third second, each light bulb numbered as a multiple of 3 changed its original bright and dark state, that is, the light turned dark and the dark turned bright; Generally speaking, every light bulb numbered as a multiple of n will change its original bright and dark state in the nth second. Continue like this, every 4 minutes.

Q: At the 200th second, how many bright light bulbs were there? .

2. The third grade mathematics knowledge volume

I don't know which version of your textbook is for the third grade. The knowledge points in the second volume are arranged in the score section: 1. Significance of score: divide the unit "1" into several parts on average, and the number representing one or more parts is called a score.

The number representing one of them is called a fractional unit. For example, 23 is to divide a whole into three parts and take two of them.

The fractional line of numerator (indicating how many parts to take) and denominator (indicating how many parts to divide an integer) 23 has a decimal unit of 13, which has two such decimal units. 2. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.

For example: 1 3 = 26 = 39 = 4121620 = 810 = 453, the comparative size of the score: (1) Compared with the denominator score, the larger the numerator, the larger the score. For example, (2) Compared with the molecular fraction, the smaller the denominator, the greater the fraction.

For example, (3) compare scores with different numerator and denominator, and first convert those with the same component mother before comparing. Such as: 4. Fraction addition and subtraction: (1) Fraction addition and subtraction with denominator, denominator unchanged, numerator addition and subtraction.

For example: 25+35 = 55 =189-19 = 79 (2) Fractions with different denominators are added and subtracted, and then added and subtracted. For example, the decimal part: 1, and the concept of decimal: numbers like 5.83, 12.5, 16.72 and 0.8 are called decimals.

2. Name of the decimal part: read: 56.833. Decimal comparison size: decimal comparison size, first compare the integer part, the bigger the integer part, the bigger it is; If the integer parts are the same, compare the first place of the decimal part; If the first digit of the decimal part is the same, compare the second digit of the decimal part ... such as 4. Decimal addition and subtraction: vertically add and subtract two decimal places, and the decimal points are aligned. Such as direction and position 1. In real life, we judge that the direction is to get up in the morning and face the sun, with the east in front, the west behind, the north on the left and the south on the right.

2. South and North are opposite, and East and West are opposite. 3. Maps are generally drawn from four directions: north, south, left and right.

Translation and rotation 1, translation: both the elevator and the cable car move in a certain direction as a whole, which is called translation. Such as: raising the national flag; Pull the drawer; The movement of the elevator; Cable car, etc.

2. Rotation: When the windmill and fan rotate, the position is fixed and always rotates around a fixed point. This phenomenon is called rotation. Such as: the rotation of the ferris wheel; The rotation of the hour hand, minute hand and second hand on the clock face; Screw the bottle cap, etc.

3. Axisymmetric figure: A figure with two sides folded in half and completely overlapped is called an axisymmetric figure. The straight line where the crease lies is called the symmetry axis.

Such as rectangle, square, circle, etc. Multiply two digits by two or three digits 1 and find the sum of several identical addends by multiplication.

What's the total of eight fifties? What is 50*8=400 10 90? 90* 10=900 2. Find the multiple of a number and calculate by multiplication. What is 20 times of 14? 14*20=280 The area of a rectangle or square is 1, and the size of the surface or closed figure of an object is called their area.

2. The relevant formula of the square: the circumference of the square = the side length * 4; Side length = perimeter ÷ 4; Area of a square = side length * side length. 3. Rectangular correlation formula: the circumference of a rectangle = (length+width) * 2; Length = perimeter ÷2- width; Width = perimeter ÷2- length.

Area of rectangle = length * width; Length = area ÷ width; Width = area ÷ length. 4. Area unit: (1) The propulsion rate between every two adjacent length units is 10.

1 m = 10 decimeter; 1 decimeter = 10/0cm; 1 m = 100 cm 1 m2 = 100 square decimeter; 1 square decimeter = 100 square centimeter; 1 m2 = 10000 cm2; 1 km2 = 100 hectare; 1 hectare =10000m2; 1 km2 =1000000m2 ... km2 hectares □ m2 decimeter square centimeter square millimeter Unit 1 Location and direction l Knowledge points: (1) Know eight directions: east, south, west, north, northeast, southeast, northwest and southwest.

1. How to tell the direction: You can tell the direction with the help of things around you, such as the sun, or with the help of tools such as a compass. 2. Be able to determine the other seven directions according to one direction and know which directions are relative.

South-north, west-east; Northwest-southeast, northeast-southwest. 3. Know the direction on the map: up north, down south, left west, right east.

(Book: Exercise 1, questions 3 and 4; 4. Understand the method of drawing a simple schematic diagram: first determine the observation point, draw the selected observation point in the center of the plane, and then determine the direction of each object relative to the observation point. Draw on paper according to "up north, down south, left west, right east" and mark the north with the arrow "↑".

(Book: Exercise 2, Question 2. ) 5. And can read the map.

P4 Example 2: Know the direction of a building or place on the whole map, and the positional relationship between two places on the map: who is in whose direction, etc. Big Ben p 1 double base training. (2) Look at the simple road map to describe the walking route.

1. Look at the simple road map: first determine your position, take your position as the center, then determine the direction of the destination and the surrounding things according to the law of going up north, down south, left west, right east, and finally determine the route to take according to the direction and distance of the destination. 2. Method of describing the walking route: Based on the starting point, see which road leads to the destination, and finally describe the walking route (where to go first, then where to go).

Sometimes you have to explain how far it is. (Book: p5 Do it; P9 did it; (Big Ben: 1 and 2 questions on the left of p3; Question 65438+ right 0, 2, 3; Comprehensive topic: give a road map, tell the way out of a place, and work out the time, speed, or arrival time, how much it costs to buy a ticket, etc. According to the information.

(Big Ben: the P5 problem 1 and 3. ) The division of the divisor of unit 2 is a single digit L Knowledge point: (1) Oral division 1. Oral calculation method of dividing whole thousand, whole hundred and whole ten by one digit (P 14 cases 1) (1) Division calculation in the table: the number before dividend 0 is divided by one digit, and.

(2) Multiply first and calculate division: See how many times a number is equal to the dividend.

3. Elementary mathematics knowledge (the more, the better)

The analysis and summary method of the trial quotient (1) divides the divisor by the whole hundred. We should divide the divisor by looking at the whole hundred.

For example,1902 ÷197 =1456 ÷ 202 = think:197 ≈ 200 think: 202 ≈ 200 200 * 9 =1876;. 400 determine the test quotient 9 determine the test quotient 7 Do: Do: because: 65438 to do this kind of questions, we must first strengthen students' oral training in multiples of150,250,350 ... This is a trial. Secondly, it should be used flexibly in calculation.

For example, 765 ÷ 247 = 567 ÷152 = think: 247 ≈ 250 think:152 ≈150250 * 3 = 750150 * 3 = 40. We can take the maximum and minimum value of the divisor (whole hundred), then find the quotient respectively, and then find the average value of the sum of the two quotients.

This average is the quotient we require or very close to what we require. For example, 781÷1361316 ÷ 261thought: because: 78 1÷ 100 quotient 7 because.

(4) How to reduce the number of trial quotients is the purpose of skillful quotients. Because we use the approximate method, the trial quotient may be larger or smaller.

At this time, teachers should explain to students the reasons for the changes in quotient and analyze and summarize the changes. (1) After the divisor is rounded, the quotient may become larger. (2) After the divisor is rounded, the quotient may become smaller and smaller. The purpose of the above analysis is to enable students to quickly classify when doing multi-digit division and find corresponding methods.

So as to achieve skillful quotient and improve accuracy and speed. Of course, students should be able to do business accurately and quickly in order to achieve the effect of proficiency in business.

Besides mastering the correct methods, we should practice more. As the saying goes, "Practice makes perfect", so proper practice is a necessary condition to improve the accuracy and speed of calculation.

Interesting math problem 1. There are 48 students participating in three sports competitions, but the number of participants in each activity is different, and there is a number "6". How many people participated in each of the three sports competitions? Longlong and Liangliang go to the park to play and want to buy tickets, but they don't have enough money. Longlong lacks 4 yuan by 80 points, and Liangliang lacks 1 point. Their money together is still not enough. How much is the park ticket? How many minutes does it take for three people to eat three tomatoes and six people to eat six tomatoes at the same time? 4. There are 10 cards, face up, 6 cards at a time. How many times have you turned the cards? Can all the cards face up? Xiao Zhang bought 24 bottles of soda, and every four empty bottles can be exchanged for 1 bottle of soda. How many bottles of soda can Xiao Zhang drink? Age problem 1. The sum of the four people's ages is 77, and the youngest is 10. The sum of the ages of the oldest and youngest people is seven years older than that of the other two. How old is the oldest person? On my father's 50th birthday, my brother said, "When I grow to my brother's present age, the sum of my brother and I will be equal to my father's then age." So how old is my brother this year? The average age of Party A, Party B and Party C is 42 years old. If Party A's age is increased by 7 years, Party B's age is doubled, and Party C's age is reduced by half, which is equal. How old is Party A? In a family, the total age of all members is 73 years old. There are father, mother, a daughter and a son at home. Father is 3 years older than mother, and daughter is 2 years older than son. Four years ago, the total age of all the people in the family was 58. How old is each member of the family now? 5. 10 years ago, Wu Hao was seven times older than his son. 15 later, Wu Hao is twice as old as his son. How old are the father and son now? Fill in the horizontal type 1. Fill the seven numbers 0~6 in the back ○, and the two-digit integer formula appears exactly once for each number. ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○967

□ 7 * □ = 6 □ =□ 3 -□□□ 4. Fill the nine numbers 1~9 in the blanks of the following formula respectively. One of the numbers is known, and only one number can be filled in each blank, so the formula is established: □□□□□□□□□ =□-75.65438. She changed all twenty cents into five cents, and the total number of coins became 73. Then she changed a penny into an equivalent nickel, and the total number of coins became 33.

Then there is a dollar in her piggy bank. 2. Three kinds of insects *** 18, * * * have 20 pairs of wings 1 16 legs.

Among them, each spider has 8 legs and no wings, each dragonfly has 2 pairs of wings and 6 legs, and cicada has 6 legs. How many are these three kinds of insects? 3. A math test paper has only 25 multiple-choice questions.

Get 4 points for doing a right question, and deduct 1 point for doing a wrong question; If you don't do it, you won't score or deduct points. If Xiao Ming gets 78 points in the exam, then he will do the right questions and the wrong questions, and will not do them.

4. A magazine, 2 yuan 50 cents per issue, once a year 12. Some students in a class book for half a year, and some book for a whole year, and they want 1320 yuan. If you book the whole year for half a year and the whole year for half a year, then * * * needs to book 1245 yuan.

How many students are there in this class? It is known that students A, B and C * * have solved 100 math problems, and each of them has solved 60 of them. If the problem solved by only 1 person is called "difficult problem" and the problem solved by all three people is called "easy problem", how many ways are there for "difficult problem" than "easy problem"? Grade three exercises 1. Calculation: 9998+998+99+62. Calculate174+177+183+182+176+18. 4.7 The average number is 28. If these seven numbers are arranged in a row, the average of the first four numbers is 26, and the average of the last four numbers is 33. What's the fourth number? 5. 1,2,6,2。

4. Knowledge points of the third volume of mathematics

Mathematics knowledge of Grade Three (Volume II) requires that the position and direction of Unit One 1 be opposite, (east and west), (south and north), (southeast and northwest) and (southwest and northeast).

Facing south, left to east, north, left to west, east, left to north, west, left to south. 2. Maps are usually drawn by (upper north, lower south, left west and right east).

Generally speaking, there are eight directions: east, west, south, north, southeast, northwest, southwest and northeast. I can read the simple road map and describe the walking route.

Mark the southeast, northwest first when you do the problem. Be sure to write clearly where you are going, how many meters you have walked, where you are going and which direction you are going.

Pay attention to the change of direction when turning. To judge the direction of a place, we must first find a symbol drawing the word "meter" at the central point (observation point), and then make a judgment. The compass is used to indicate the direction. One hand always points to the south and the other hand always points to the north.

5. Orientation knowledge in life: ① The Big Dipper is always in the north. The shadow is opposite to the direction of the sun.

The sun is in the east in the morning, in the south at noon and in the west at night. (4) The wind direction is opposite to the direction in which the object inclines.

(When the wind blows, the trees bend in the opposite direction, and the smoke floats in the opposite direction ...) China is located in the northern hemisphere, with lush leaves in the south and sparse leaves in the north. The divisor of the second unit is the division of one digit 1. As long as it is an average score, it is a division calculation.

2. Rule of vertical division with divisor as one digit: (1) Starting from the high-order division of dividend, try the first digit of dividend with divisor every time. If it is less than the divisor, try the division of the first two digits again. (2) Write the quotient except the dividend on the dividend.

(3) For each quotient, the remainder must be less than the divisor. Mandarin: The divisor is one. Look at the first one, and one is not enough to look at two. Comparing every division except quotient, the remainder is less than the divisor.

3. There are several zeros at the end of dividend, and there are not necessarily several zeros at the end of quotient. (For example, 30÷5 = 6)4. Written division: (1) remainder must be less than divisor.

In division with remainder: the minimum remainder is1; The maximum remainder is divisor minus1; The smallest divisor is the remainder plus1; Maximum dividend = quotient * divisor+maximum remainder; Minimum dividend = quotient * divisor+1; (2) Check the calculation of division: → Divide the remainder by the multiplication divider/divider = quotient divider/quotient * divider = divider divider/divider = divider/divider/divider = divider (divider-remainder)/quotient 0 multiplied by any number to get 0; 0 plus any number gets any number itself, and 0 minus any number gets any number itself. 5. Division sequence by stroke: determine the number of digits of quotient, try quotient, check, check.

6. When calculating the division with a pen, if the quotient of digits is not enough 1, add a zero. (If the division of the highest bit is not enough, just retreat one bit and negotiate again. )

7. Multi-digit divided by one digit (judging how many digits the quotient is): compare the number on the highest digit of the dividend with the divisor. When the number on the highest digit of the dividend is greater than or equal to the divisor, how many digits is the quotient of the dividend; When the highest digit of the dividend is less than the divisor, the digit of the quotient is the digit of the dividend minus 1. Unit 3 Composite Statistical Table The characteristics of composite statistical table are: it is conducive to the comparison of data, and it is easier to distinguish the differences of the same items.

The product of two digits multiplied by two digits in cell 4 1 and two digits multiplied by two digits may be (3) digits or (4) digits. 2. Oral multiplication: Multiply the integer ten and the integer hundred, just multiply the previous number, see how many zeros there are in the two factors * * *, and then add a few zeros at the end of the result.

3. Estimate: 18*22. You can calculate the factor as an integer of ten or one hundred. One factor can be regarded as a divisor, or two factors can be regarded as a divisor at the same time. )

4. Generally speaking, it should be estimated. 5. If you have asked enough questions, can you wait? There are three steps: ① calculation, ② comparison and ③ answer.

→ Don't forget to compare this step. 6. Written multiplication: multiply the first factor by the number on the second factor, and then multiply by the number on the tenth factor.

7. Related formula: factor * factor = product ÷ factor = another factor operation order: multiply first and then divide, then add and subtract; Operations at the same level should be calculated from left to right; If there are parentheses, calculate the operation in parentheses first. The area of the fifth element is 1, and the size of the curved surface or closed figure of the object is their area.

The length of a closed figure is called perimeter. The units of length unit and area unit are different and cannot be compared.

2, compare the size of the two graphics area, to use a unified area unit to measure. 3.① A square with a side length of 1 cm and an area of 1 cm 2; ② A square with a side length of 1 decimeter and an area of 1 square decimeter; ③ Square with side length 1 m and area 1 m2; 4. Rectangle: area of rectangle = length * width of rectangle = (length+width) *2 Find length: length = area of rectangle ÷ width of known perimeter: length = perimeter of rectangle ÷2- width: width = area of rectangle ÷ width of known perimeter: width = perimeter of rectangle ÷. 4 side length: side length = square area ÷ side length = square perimeter ÷45, and the ratio between length units: 1 cm = 10 mm 1 decimeter = 10 cm 1 m = 65438.

The perimeters of two rectangles with equal areas are not necessarily equal. 7. Find examples that are close to 1 square centimeter, 1 square decimeter and 1 square meter in life.

For example, 1 cm2 (nail cover), 1 cm2 (computer disk A or wire socket) and 1 m2 (small display board beside the classroom). 8. Distinguish between length units and area units: length units measure the length of line segments and area units measure the size of surfaces.

(2) area calculation of rectangle and square 1. Classification: What kind of problem is finding the perimeter? (Sewing lace, fences, railings, the length of paths around ponds or flower beds, the length of running around the playground, etc. What kind of problem is finding the area? Or is it related to the area? (textbook cover size, wall painting, path area around flower bed, glass of dining table, tablecloth of desk, floor sprinkled by sprinkler.

5. Sort out the knowledge points of the second volume of mathematics in the third grade of primary school.

First, the problem of planting trees: this kind of application problem is titled "planting trees".

Any application problem of studying the four quantitative relations of total distance, plant distance, number of segments and number of plants is called tree planting problem. The key to solving the problem: to solve the problem of planting trees, we must first judge the terrain and distinguish whether the graph is closed, so as to determine whether to plant trees along the line or along the perimeter, and then calculate according to the basic formula.

Law of solving problems: planting trees along the line = total distance ÷ plant distance+1 plant = number of segments+1 plant distance = total distance ÷ (tree-1) total distance = plant distance * (tree-1) planting trees along the perimeter = total distance. Later, it was completely revised and only 20 1 was buried.

Find the distance between two adjacent ones after modification. Analysis: this question is to bury telephone poles along the line, and the number of telephone poles is reduced by one.

The formula is 50 * (301-1) ÷ (201-1) = 75 (m) 2. Application of Fractions and Percentages 1 Fractional addition and subtraction application problems: Structural and quantitative application problems of fractional addition and subtraction and integer addition and subtraction. 2 Fractional multiplication application problem: refers to the application problem of finding the fraction of a given number.

Features: The quantity and fraction of the unit "1" are known, and the actual quantity corresponding to the fraction is found. The key to solving the problem is to accurately judge the number of units "1".

Find the score corresponding to the required question, and then formulate it correctly according to the meaning of multiplying a number by a score. 3 fractional division application problem: find the fraction (or percentage) of one number to another.

Features: Knowing one number and another, find the fraction or percentage of one number. "One number" is a comparative quantity, and "another number" is a standard quantity.

Find a fraction or percentage, that is, find their multiple relationship. The key to solving the problem: start with the problem and find out who is regarded as the standard number, that is, who is regarded as "unit one" and who is the bonus compared with the number of unit one.

A is the fraction (percentage) of B: A is the comparative quantity and B is the standard quantity. Divide A by B .. How much (or how few) is A more (or less) than B? A minus B is more (or less) or (how many) than B. ..

Relationship (A minus B)/B or (A minus B)/A. Given the fraction (or percentage) of a number, find this number.

Features: Knowing an actual quantity and its corresponding fraction, find the quantity with the unit of "1". The key to solve the problem is to accurately judge the number of units "1". The quantity of unit "1" is regarded as the equation of X according to the meaning of fractional multiplication or the equation of fractional division, but the known actual quantity corresponding to the fractional rate must be accurately found.

Iii. Measurement 1. Length (1) What is length? Length is a measure of one-dimensional space. (2) The conversion between commonly used unit kilometers (km), meters (m), decimeters (dm), centimeters (cm), millimeters (mm) and microns (um) is 1mm = 1000 microns, 1cm = 65438. 1 m = 1000 mm, 1 km = 1000 m2. Area (1) What is the area, that is, the size of the plane occupied by the object?

The measurement of the surface of three-dimensional objects is generally called surface area. (2) Common area units square millimeter, square centimeter, square decimeter, square meter and square kilometer (3) Conversion of area units 1 square centimeter = 100 square millimeter, 1 square decimeter = 100 square centimeter, 1 square meter =/.

Volume, the volume of objects that can be accommodated in boxes, oil drums, warehouses, etc. , usually called their volume. (2) Common units: 1, unit of volume cubic meter, cubic decimeter, cubic centimeter 2, unit of volume: liter, millimeter (3) Unit conversion (1) unit of volume 1 cubic meter = 1000 cubic decimeter 1 cubic centimeter (.

(II) Common unit tons: tons and kilograms: kilograms and grams (III) Common converted tons = 1 000kg1kg =1000g V. Time (I) What is time refers to a period of time with a starting point and an ending point (II) Common units: century, year, month and day. Seconds (3) unit conversion 1 century = 100 1 year =365 days (average year) 1 year =366 days (leap year). One, three, five, seven, eight, ten and twelve are big months. There are 29 days in February of leap year, 1 day = 24 hours, 1 hour =60 minutes, 1 minute =60 seconds. The intransitive verb money (1) What is money? Money is a special commodity, which acts as the equivalent of all commodities. Money is a general representative of value and can buy any other commodity.

(2) Common units, angles and minutes (3) Unit conversion 1 yuan = 10 angle 1 angle = 10 minute.

6. Junior high school math knowledge

Key points of mathematics knowledge in the second volume of the third grade of primary school

I. Location and direction

Eight directions: east, south, west, north, northeast, northwest, southeast and southwest:

Second, the year month day:

(1) The Gregorian year is a multiple of 4, which is generally a leap year, but the Gregorian year is an integer, and it must be a multiple of 400 to be a leap year. For example, 1900 is a normal year, not a leap year, and 2000 is a leap year, not a normal year.

(2) February 29th in leap year and February 28th in normal year. In other months, the big month is 3 1 day and the small month is 30 days.

(3) 1 year has 12 months, with 365 days in a normal year and 366 days in a leap year.

(4) The difference between the 24-hour system and the 12-hour system at the same time is 12.

Three. Area and perimeter

(1) area: the size of an object surface or a closed figure;

(2) Perimeter: the length of the closed figure.

(3) The perimeter of a rectangle = (length+width) *2, and the perimeter of a square = side length *4.

(4) Area of rectangle = length * width, and area of square = side length * side length.

Four. Average and decimal

(1) average = sum of all data ÷ number of data.

(2) Numbers like 0.2, 1.8 are called decimals.

Five, commonly used units and their rates.

1, RMB unit (Yuan, Jiao and Min):

(1)1yuan = 10 angle; 1 angle = 10 point; 1 yuan = 100 integral;

② 1 min =0. 1 angle; 1 angle =0. 1 yuan;

2. Length unit (kilometers, meters, decimeters, centimeters, millimeters):

① 1k m = 1000m； 1 m = 10 decimeter; 1 decimeter = 10/0cm; 1 cm = 10/0mm;

② 1m = 100cm = 1000mm；

③ 1mm = 0. 1cm； 1 cm =0. 1 decimeter; 1 decimeter =0. 1 meter;

3 area units (square kilometers, hectares, square meters, square decimeters, square centimeters, square millimeters):

(1)1m2 = 100 square decimeter; 1 square decimeter = 100 square centimeter;

② 1 km2 = 100 hectare; 1 hectare =10000m2;

7. Extracurricular mathematics knowledge

1. Goldbach conjecture 1742 Goldbach in Germany wrote a letter to Euler, a great mathematician living in Petersburg, Russia at that time. In the letter, he raised two questions: First, can every even number greater than 4 be expressed as the sum of two odd prime numbers? Such as 6 = 3+3, 14 = 3+ 1 1 and so on. Second, can every odd number greater than 7 represent the sum of three odd prime numbers? Such as 9=3+3+3, 15=3+5+7, etc. This is the famous Goldbach conjecture. This is a famous problem in number theory, which is often called the jewel in the crown of mathematics.

2. A long time ago, there was a man named Caesar in India. He carefully designed a game for the king, which is now 64-square chess. The king was very satisfied with the game and decided to give it to Cesar. The king asked Cesar what he needed. Cesar pointed to the small squares on the chessboard and said, "Just give me the first square 1 grain of wheat, the second square with 2 grains of wheat and the third square with 4 grains of wheat. At this rate, the wheat in each square is twice as much as that in the previous one. Your Majesty, give me all the 64 tablets that fill the chessboard like this. " The king readily agreed to Cesar's request without thinking. However, after calculation, ministers found that it was not enough to give Cesar all the wheat harvested in one year. Cesar is right. His demands can't really be met. According to the calculation, the total number of wheat in 64 squares on the chessboard will be a 19 digit, which is about 200 billion tons by weight. The king has supreme power, but he interprets the profoundness of knowledge with his ignorance.

3. How did the wise men in ancient Greece measure the height of the pyramids? First, a bamboo pole is erected on the ground, and the length of the shadow of the bamboo pole and the shadow of the pyramid are measured at the same time when the sun is shining, and then the ratio of the length of the bamboo pole to the shadow of the bamboo pole is calculated, that is, the ratio of the height of the pyramid to the length of the shadow of the pyramid. Using this ratio and the shadow length of the pyramid, the height of the pyramid can be calculated.