The basic requirement of the premise division method is that there is no difference between elements, and it can be directly divided into three parts by two divisions. However, the partition insertion method just connects these steps together.
Similar to the pigeon hole principle.
Imagine putting a ball separated by the first partition in the first pocket, a ball in the drawer, a ball in three different bags, the remaining number of balls C (greater than or equal to one) in the third pocket, and then B balls separated by the second partition in the second pocket, but the bags are different: the balls are the same, that is to say, there is no need to change positions between elements.
Give a very simple example!
2. Insert narration to write a 400-word composition. Six years of primary school seems to be a long but short time. I have left many unforgettable memories here. The most unforgettable thing is the deep and pure friendship between my classmates and me.
Every time we have a break, there is always a hearty laugh in our class. That man is my good buddy-Zhao Yuxiong. He has short hair, a Chinese face, faint eyebrows and a pair of eyes full of curiosity. He looks like a "living fairy" all day. The expression on his face is always sunny.
Looking back on the scenes in the past six years, I am very moved.
I remember that after the final exam of grade three, the teacher punished me for my summer homework. I found a place in it that was not clearly printed, so I wanted to borrow it from Lao Zhao. But Zhao Yuxiong went to the choir to sing, so I found the exercise book in his schoolbag and took it away. Unexpectedly, just as I was about to return it to him, his exercise book disappeared. I was in a hurry. I searched everywhere, but I still couldn't find it. Zhao Yuxiong is back. He rummaged through his schoolbag and seemed to find that his notebook was missing. I went over and said, "Brother Zhao, I don't know what to say." He was puzzled and asked, "What is it?" "I ... I lost your book ..." I think Zhao Yuxiong must be angry. I was waiting for the storm, but to my surprise, he just sighed deeply and said nothing. When I saw it, I quickly knelt on the ground with my hands clenched and said respectfully, "Thank you for not killing me. I will never forget it." Then he smiled.
After the summer vacation, I went back to school and an incredible thing happened. Zhao Yuxiong didn't buy a new one himself, but borrowed one from others. Every time I think about it, my heart is warm. He is really my good friend.
I remember another time, when I was in the fifth grade, my composition level was below average in my class. My composition is always written after sitting down. My good buddy Zhao Yuxiong volunteered to help me correct my composition. After class, I sat in front of him, listened to his advice and carefully revised my composition. Even if it is a punctuation mark, he must carefully consider it, and no typo can escape his eyes. Zhao Yuxiong ignored Rao Shuai, who called him again. His determination to correct my composition remains firm. He refused him with a humorous sentence: "Sorry, the subscriber you dialed is helping people to correct their composition. Please redial later." We all laughed. Rao Shuai left, and with the help of Zhao Yuxiong, my composition finally entered the book. There are not only the handwriting left by the teacher, but also all the blue pages left by Zhao Yuxiong.
Endless stories, classmates' feelings, even if the innocent life of primary school is over, these lovely images will remain in my heart forever. Maybe we will never be together again, but I am willing to keep this friendship in my heart! Forever, forever ...
3. Insert the narration (three things) to write an unforgettable composition. Memories always dance a flying dream to naughty butterflies in the air, then disappear on the time axis, and then inadvertently break into your world. -inscription
Time flies, time flies. June, which once made me cry, has quietly left. Until now, I still can't believe that the days when we struggled together, sweated together and shed tears together ended in June, the season of parting. What a time it was, what a youth!
Those who recite with small flashlights under the covers before dawn, those who March into the small flower bed with English textbooks in the newly awakened sun and read unscrupulously, those who pester the teacher to solve problems after class to make up for their lack of legs, and those who run back to the dormitory with books in their arms after the teacher drives us every night ... Now they laugh so calmly. However, those feelings are hard to remember, leaving a strong trace in life. The time when tears and sweat danced alone is enough for people to remember for a lifetime. What beautiful dreams are we having all those days and nights?
I believe that most people in junior high school have experienced it. Because of fear, they failed again and again and had to stand up. Because of fear, pestering teachers to solve problems after class; Because of fear, I dare not go back to the dormitory earlier than others; Because of fear, so a person hiding in the room secretly wipe tears; Because of fear, I dare not ask when the results will come out; There is only one purpose, the senior high school entrance examination! After the battle, I felt a burst of melancholy and joy.
Just a few months ago, I was still worried about the senior high school entrance examination. Today, I was sitting in a high school classroom, watching the clouds light and the wind light, and watching the chalk in the teacher's hand brush on the blackboard. Yes, I have crossed the threshold of high school, which is the first stop in my life. I can't say that I am a proud winner. Perhaps it is a great regret in my life that I did not enter my sacred high school. But every day from today is under my control, and I still have the opportunity to try my best to fight for the next goal. This is not the end of high school, but another starting point. A bigger test is waiting for me. The beautiful dream of the university came to my mind today and I saw the university waving to me.
Looking back on three years, this kind of life is very worthwhile. There won't be too much sadness, beauty and emptiness when recalling, and youth is fleeting. Don't be idle, grow old together, don't waste this beautiful youth, raise the flag and March forward. Wait until the day of victory, let memories fly and tears splash.
4. Write a 500-word composition in flashback, and write a composition in flashback. About 500 words.
I only hide in your arms, in winter, with a faint smile on my face and her caring eyes. However, this still can't stop her from loving me, and then send me out with concerned eyes, showing endless love.
Mother's eyes always reveal infinite care, and she can't help frowning and doing it in winter? "I didn't care, and it became a series of brilliance." Every time I read this little poem by Bing Xin, it seems to remind me to be careful on the road and let me bathe in it. My mother always looks at my maternal love with loving eyes.
"mom. In my impression, in my mind, whenever I walk alone; When I was older, my mother sent me to school: "I forgot to wear it." When I put it on, I couldn't help but see my mother's face, but I knew it was painful. My mother's hand was bleeding. Once, so I don't want to listen to it, although my mother no longer watches me walk like a child. " But my mother insisted on handing me her gloves, which were soaked with thick maternal blood. However, my mother's non-negotiable eyes finally made me put on those gloves with her body temperature, which were full of maternal love. A pair of hard-working hands seem to clear the obstacles ahead for me! The wind and rain in the sky are coming! "I was very touched, my mother told me first. Her eyes sparkled with wisdom; The storm in my heart is coming and I feel extremely happy.
My mother is a middle school teacher. One wrinkle after another on her face. The bird hid in its nest and let me lie in this cradle happily, with heavy elegance. My eyes are moist. ...
Bathed in this warm maternal glow. Suddenly. When I was very young, I carried a strong maternal love; The way of "ordering" now. The north wind blew in waves, but it was not cold anyway: "why didn't I wear gloves?" I always knew that my mother's hands couldn't hold the cold wind, and she was watching me move forward on the road of life ... "
Mother's hands are the carrier of her deep maternal love. My mother's hands are rough, so I don't have to wear them. When I can go out alone, she looks back at me with my bare hands, the north wind is blowing, and my eyes and hands are connected in series. My mother wove a warm cradle for me with her deep maternal love.
5. The interpolation method, binding method and element priority method are introduced in detail with examples.
"Non-adjacent problem" interpolation method, that is, when solving the problem that some elements require non-adjacent, first arrange other elements, and then insert the specified non-adjacent elements into the gaps or positions at both ends of the arranged elements, thus solving the problem.
Example 1. If there are five people in the queue, A, B, C, D and E, how many queuing methods are there?
Analysis: The topic requires that A and B must be separated. First of all, there are six arrangements of C, D and E. If arranged according to D C E, there are four vacancies in the middle and both ends of D, C and E, that is, ︺ D ︺ C ︺ E. At this time, A and B can be inserted into any two of the four vacant positions, and A (4 4,2) is used. According to the multiplication principle, * * has 12*6=72 queuing methods.
Example 2. There are six programs in the program list. If the relative order of these programs remains unchanged and three programs are added, how many different ways are there?
Analysis: It is troublesome to answer directly, so you can solve the problem by interpolation, so you can insert 7 vacancies with one program first (after the original 6 programs are arranged, there are 7 vacancies in the middle and at both ends), and there is a way; One method is to insert 8 vacancies with another program; There are nine ways to insert nine vacancies with the last program, which is obtained by multiplication principle: all different addition methods are =504 [1].
Tip: When solving the permutation and combination problem by interpolation, we must pay attention to the interpolation position including the "middle vacancy" and "two-end vacancy" of the elements arranged first. The process of solving problems is "arrange first, then insert empty".
Binding method
Binding methods are used for adjacent elements. That is to say, when solving the problem of requiring several elements to be adjacent, we should first consider the adjacent elements as a whole, and then consider the order between elements in the meta-element. The binding method is the solution strategy. [Note] When solving the permutation and combination problem by binding method, we must pay attention to the order problem in the "binding" of large elements. Example: There are 8 different books; Among them, there are 3 math books, 2 foreign language books and 3 books on other subjects. If these books are arranged in a row on the bookshelf and math books are put together, there are () ways to put foreign documents together. Solution: If three math books are tied together as a whole, two foreign documents are also tied together as a whole. Three math books are arranged in (3,3), and two foreign language books are arranged in (2,2). According to the principle of step-by-step counting, there are arrangement methods A (5,5) A (3,3) A (2,2) =1440 (species). How many different ways are there to put six balls into five boxes? In fact, according to the pigeon hole principle, there must be two balls together. So the answer is that c (6,2) x a (5,5) is actually the product of 2 and 5 in 6. Example 2: Class 3, Grade 5 held a Children's Day Gala. The whole activity consists of 2 dances, 2 singers and 3 sketches. Excuse me, how many [1] different appearances are there if the same type of program is required to be performed continuously? A: If you need to play the same type of programs continuously, you can use the "bundling method". First, fill the three programs of dance, singing and sketch, and then arrange the order of specific programs within each program. Therefore, the total number of occurrences is: a (3 3) * a (2 2) * a (2 2) * a (3 3).
As for the element priority method, it seems that there is no such method in mathematics. Do you have the wrong number?
6. Motherly love: composition written with parenthesis 150. This is a description of the mother's hand, not an insertion.
But what good hands! The fingers are thick and short, the palms are covered with calluses, and the palm prints have become dense and criss-crossed, and a layer of mud will never be washed away. Like dried pine bark, like the bottom of a mud pond that cracks like a hole.
The palm of your hand is covered with calluses and the back of your hand is wrinkled. Deep cuts will appear on your fingers in winter. At this time, my mother will wrap her fingers with a band-aid to relieve the pain of washing dishes and clothes.
This will do.
True love is low-key and silent. I had never found my mother's love so deep before, until that day I met an old friend on the road.
"Why don't you even button up when you go out?"
I was shocked by his question, and I was a little embarrassed to answer: "It was careless to rush out and find a button missing from this shirt."
I used to live with my mother and always enjoyed her care, but I didn't find that her behind-the-scenes efforts were so meticulous. At any time, shirts are neatly hung in the cupboard, and you can go out with sleeves. Her love is reflected in the fact that there is always hot and cold water at home. Her love is reflected in the fact that there are always sweaters knitted by her in my closet and traces of buttons sewn by her. If you feel bad, you can change it yourself. )
My mother will always occupy the softest and warmest corner of my heart.