Today is another sunny day. I was wandering in the street when I suddenly saw a lot of people gathered not far away. I ran for a year, and the result was a prize-winning game. "Hum, what's fun about winning the prize?" I was bored when the person next to me quickly said, "It's not fun to grab the prize, but there is a big prize that can attract people." I asked eagerly, "What is it!" "50 yuan money." The man with big eyes said. I'm very excited to hear that. "I have to try anything for such an attractive prize." Then I asked the shopkeeper how to catch it. The shopkeeper said, "This is 24 Mahjong, and it says 12 5, 12 10. You can only catch 12 mahjong at a time. If the total number of 12 mahjong targets is 60, then you can win the 50 yuan Prize. " Without rolling up my sleeves, I took out 5 yuan money from my pocket and gave it to the shopkeeper.
Although I won 10 times, I still didn't win the grand prize.
When I got home, I thought about it and felt something was wrong. I think, to get 60 points, all 12 mahjong should be marked with 5. In the best case, the first 1 second catch 1 5, the second catch of two 5 s and the third catch of three 5 s will cost at least 6 yuan money. But what if the target number of mahjong is 10 or the sum of the two is the same, how many times will it cost?
Finally, after some consideration, I finally figured it out. I rushed to the street to look for an account, but I ran away without a trace.
Saturday, February 28th is fine.
When I read the newspaper today, I saw such a topic: Find the surface area of a cone.
[Title] A cone, the diameter of the bottom surface is 6 meters, and the length from the apex of the cone to any point on the circumference of the bottom surface is 5 meters. Find the surface area of this cone.
Although I have never learned to calculate the surface area of a cone, I have learned the surface area of a cylinder. By solving the surface area of cylinder, I know that the surface area of cylinder is equal to one side plus two bottom areas, while the surface area of cone is one lateral area plus one bottom area, and the side is a sector. Although I haven't studied it, I have checked the data and know that the area of a sector is: the area of a sector = arc length × circle radius × 1/2. The topic has told us that the length from the apex of the cone to any point on the circumference of the bottom surface is 5m, while the arc length is 3. 14×6= 18.84 (m), and the sector area is18.84× 5×1/2 = 47./kloc.
Mathematics is the gymnastics of thinking. As long as we study hard and think hard, we will certainly overcome the problems and embark on the road to success!
Tuesday, 2 March
Every time I go to Tomb-Sweeping Day, there will be a sea of people on the giant mountain, so some swindlers come up with some deceptive tricks, such as gambling on something on a plate.
Prop is very simple, draw a big circle on a board, and fix a rotatable pointer in the center of the big circle with a nail. The great circle is divided into 24 equal squares, and the needles in the squares can rotate. The box says 1-24 equal numbers, which are worthless in the odd box, but almost all even numbers are valuable.
The gameplay is also very simple. Set the pointer to 1 first, then you dial the pointer again, and the pointer will start to rotate and finally stop in a grid. Then press the number marked on the grid where the pointer is located and dial the pointer again. N- 1 grid, where n is the number marked on the grid.
This is just a little math game. In fact, no matter which box you dial, you can only lose money, not make money. Because when the pointer turns to an odd cell, the number of cells dialed is odd-1= even, and odd+even is only equal to odd, so it is impossible to turn to an even cell and nothing valuable can be obtained. If the pointer turns to an even grid and the number of grids dialed is even-1= odd, and odd+even = odd, then you won't get anything of value.
Friday May 12
Calculate wages
At noon, my father came back from work, humming a ditty, and happily stepped into the house. I greeted him and asked, "Dad, what's so happy today?" Dad said, "I got a raise this month." I asked, "How much salary do you get now?" Dad thought for a moment, smiled and said, "My salary is higher than your mother's. Our monthly salary adds up to 2800, and the monthly salary difference is 100. How much do you think I get a month? "
After listening to my father's words, I began to draw line drawings on paper to help me understand:
Through observation and thinking, I quickly worked out the answer and told my father. First of all, mom's salary is as much as dad's, so mom and dad's monthly salary is (2800+ 100)=2900 yuan, and then the total monthly salary is divided into two parts, and 1 part is dad's monthly salary. The formula is: (2800+ 100)÷2= 1450 yuan.
Dad listened and nodded with satisfaction. At this time, my mother, who was cooking, said to me, "Do you have any other methods?" "Is there any other way?" I said in surprise. I stopped to observe and think curiously. I found that the key to this problem is to find out who is the standard. Different standards have different methods. So, I have a second method: taking mom's salary as the standard, assuming mom and dad's salary is the same, then the sum of their monthly salary is (2800- 100)=2700 yuan, and then divide the sum of monthly salary into two parts on average. 1 part is mom's monthly salary, and finally it is more than mom's 100. The formula is (2800-100) ÷ 2+100 =1450 yuan.
Tuesday, June 28th
At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:
There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.
I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?
Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.
Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.
The final result is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).
Today the teacher gave us a very complicated formula. Later, after a heated debate with students, we finally gave this formula the "correct method".
The topic is as follows: "123456789× ()+() = 98765432". As soon as the teacher wrote it on the blackboard, I began to ponder. God, this question is too complicated. Such a long number alone makes people dizzy. If we try one by one, when will it be? I'm not mistaken! Do you want to die, or do you want to face difficulties? I looked around and saw that everyone was busy. I can't be idle, can I? My brain began to run at a high speed.
Let me crack it in a complicated way first. So, I began to think carefully, what number multiplied by 9 equals the last digit plus "1"? "ah! I thought it was "9" Isn't 9 times 9 equal to 8 1? The last one is "1". So simple! I'm smart. Finally, it reminded me that I was so excited that I was about to cry. The following should be ... Just when I was enlightened by generate, my mind was disturbed by the music practiced by the radio. My mind is blank and my heart is like a desert. I don't remember anything. " Alas! The cooked swan flew away again. "I sighed sadly. But I don't give up and try to think about my position, but even if I scratch my head, I still can't figure it out. As the saying goes, "Two heads are better than one. "So, I decided to give this face to others to ask. I came to the famous Shao. To my surprise, it turns out that he is also deeply involved in this problem and is discussing it with others. I went forward to discuss with them. Shao seemed to lack confidence and whispered, "I think the first bracket should be 1, and the second bracket should be 98765432 1 minus 123456789." I patted the back of my head and screamed, "Yes! I'm really confused! But I thought about it calmly. The brackets in this question are too small to fill in so many numbers of candied haws. It is definitely not that simple! But how to calculate? Are we in trouble again?
Tuesday, June 28th
At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:
There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.
I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?
Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.
Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.
The final result is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).
Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.
I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.