For example, if the first person says 7 and the second person says 10, you get17; Then the first one says 5 and gets 22; ..... Do you think you can talk to 100? Before that, talk to 89 first. After you talk about 89, no matter what the other party says, you can talk 100. And to say 89, you have to say 78 first.

100 subtract 1 1 and you will get a series of winning numbers: 89, 78, 67, 56, 45, 34, 23, 12, 1.

This serial number is easy to remember. At the beginning, who can win? However, if the speaker doesn't know this trick, you can always occupy the winning number, step by step, and count to 100.

Math game: The game of black and white chess is set with four white pieces and four black pieces as shown in the figure. It is required to move white pieces to squares numbered 1, 2, 3 and 4, and black pieces to squares numbered 6, 7, 8 and 9. The rules for moving are:

(1) Each chess piece can reach an adjacent square at a time, or skip a square, and cannot jump forward again;

(2) No matter which chess piece can return to the grid it has been to;

(3) There cannot be more than one chess piece in each grid;

(4) jump off the white chess piece.

Twenty-four moves can make the positions of black and white pieces interchangeable;

Please think about it. Is there a better jumping method?

If there are five white pieces and five black pieces, or more pieces, how many levels do you have to jump to change places?

If there are two white chess pieces and two black chess pieces, the children in kindergarten will be interested.

Math game: How to fill four letters A in a 16-grid square so that there is only one letter A in each row, column and diagonal? Fill a letter in a square on one diagonal, and two squares that can't be filled appear on the other diagonal. These two squares are in the same row and column as the squares that have been filled with letters.

Fill the second letter in one of the other two squares on the other diagonal. According to the conditions of the topic, the two letters that have been filled in diagonally determine the position of the other two letters, which is easy to fill in. In this way, if the position of the first letter on a diagonal line is determined, there are two answers to this question. Considering that the first letter can be filled anywhere on the diagonal, there are 2× 4 = 8 answers to this question.

If the four letters are different, there are 8×24= 192 answers.

Math game: photo sequence (1) Dad, mom, brother and I take photos together. Mom is on dad's left, I am on mom's left, and my brother is on dad's right. Please tell me the order of taking pictures from left to right.

(2) Dad, Mom and Brother take a group photo together. If you take pictures in a line from left to right. What's the arrangement?

How to send newspapers

There are 26 offices in a certain unit, and the connecting line between the offices is the road connecting the offices (as shown in the figure), and the office names are represented by numbers. In order to do a good job, Xiaoming asked to deliver books and newspapers instead of the messenger Uncle Li, and Uncle Li agreed, but put forward one condition: deliver books and newspapers from the reception room, and do not take the repeated route or the repeated office, and finally return to the reception room. Do you know how Xiaoming should go?

Math game: an interesting game of train tickets. If you go out by car, suppose the number of a ticket you bought is 524 127. Don't change the order of numbers. Can you add mathematical operation symbols between numbers to make the number 100?

If several friends ride together, a race can be organized: Who gets the 100 with the number on the ticket first?

Students, I believe you have the answer.

Math game: How Magic 5 lists a formula with three 5s, and the result is equal to 1. 1=(5/5) to the fifth power. Please think about it. Are there any other answers?

Questions like this are:

(1) How to use three 5s and two s?

(2) How to use three 5' s and 4' s?

(3) How to remember 5 s with three 5s?

(4) How to record 0 with three 5s?

(5) How to use five 3 notes 3 1?

Math game: Mystery game, please secretly set an even number. After doubling, take half and double. Ok, now, just tell me the quotient divided by 9, and I will tell you the secret number right away.

Suppose the number is 6, multiply by 2 to get 18. Half of this number is 9, multiply by 2 to get 27, and divide by 9 to get 3, which is half of the number. In this game, the password can also be odd. It's just that the statement after the odd number is doubled needs to be changed a little, and it can't be divisible by 2. Add 1 and do as before.

For example, the implicit number is 5, and if it is doubled,15 is obtained; 15 plus 1 to get16; /kloc-half of 0/6 is 8; Double 8 to get 24. 24 divided by 9, quotient 2, remaining 6. Multiply the quotient 2 by 2 and add 1 to get the dark number 5. Why does it have to be like this? You can also use letters instead of numbers to prove it.

Math game: You write the number 1089 on a small piece of paper, put it in an envelope, seal it and give it to your partner. Then, let him write a three-digit number on the envelope at will, and ask that the numbers at both ends of this number are different, and the difference is greater than 1. After writing, ask him to exchange the numbers at both ends and subtract the smaller numbers from the larger ones.

In the obtained result, the numbers at both ends are exchanged, and the difference between the obtained three digits and the first two three digits is added to get a sum. Well, ask him to open the envelope and take out a small piece of paper that says 1089. To his surprise, this figure is exactly what he got.

This game, which sounds a little awkward, says: As long as (A-C) is greater than 1, GHI will always be 1089 no matter what the numbers are. Why is this happening?

Look at f first. Because A is greater than C, (C-A) is not reduced enough. Borrow 1 from b and get f =10+c-a. ..

Looking at e B- 1-B is not enough. Borrow 1 from a to get E = 10+B- 1-B = 9.

Look at d.d = a-1-C.

So, I have to

F+D = D+F = 10+C-A+A- 1-C = 9； E+E= 18 .

So GHI = 1089.

Math game: let your little friend write a three-digit number at will, ask the numbers at both ends to be different, and tell you the difference. After writing, let him exchange the numbers at both ends of this number to get another number.

Then, subtract the smaller number from the larger number, and the difference can be divisible by 9. You can always know what the quotient of this difference divided by 9 is.

The quotient is equal to the difference between the numbers at the two ends of that three-digit number and the product of 1 1. For example, 845-548 = 297,297 ÷ 9 = 33 = (8-5) ×11.

Why is this happening? One way is to count all three numbers one by one.

Another method is to imitate the answer of "a fast algorithm for finding the square" and give the proof with letters instead of three digits.

Math game: The guessing game takes the numbers from 1 to 12 and arranges them along a circle. Whoever secretly sets a number from this circle can guess it quickly. Of course, you can also guess the dark spots with 12 playing cards or with the clock.

All right. Now you let a child remember the numbers in a circle in his mind. Then, you assign him any number on this circle, and add 12 to this number by careful calculation (this is a secret, no one can know). After that, you say this number out loud, and let the person who secretly decides this number start counting from the number you specify when he wants to count it in his mind, and count one by one in the counterclockwise direction of the circle until you count it out loud. That's it. Just stop at his code.

Suppose the number in the circle is 5 and the number you specify is 9. Add up 12 and 9 by heart and you will get 2 1. Then, you said to him, "Please count silently, starting from the number you specified, starting from 9 and counting counterclockwise. Count to 2 1 and stop. " He starts from 5 and counts from 9, 9, 10, 1 1 ... and then he stops at his secret number 5. This game is a bit of a bluff. Actually, the reason is very simple. From 5 to 9 is such a number: 5, 6, 7, 8, 9; From 9 to 5, you have to go through these numbers: 9, 8, 7, 6, 5. Just count down. Add 12, count again, and return to the same number 5.

If you understand the truth, you can make up many more interesting games. For example, if you set 5 and specify 9, you can make a change and say, "Now, I'll knock on the table. Knock for the first time, you are in your mind, add 1 to your password. Knock the second time and you add 1. Go like this. Add it to 2 1 and you can say 2 1 loudly. " At this time, if you stop knocking on the table, you can point out that his password is 5.

Why can you clearly point out 5? Because when you knock on the table, you count 1, 2, 3, ... He says "2 1" and you count 16. Considering that he counts from 9, if he counts from 5, you should count to 17. Then, you start at 9, count from 1 counterclockwise to 17, and you count to 5.

Math game: Grandma's checkered cloth Grandma has two checkered cloths. One piece is 60×60 square centimeters, and the other piece is 80×80 square centimeters. She decided to use them to make a 100× 100 square centimeter plaid.

Mother accepted the job and promised to cut each piece into two parts at most, without cutting any squares. How did mom do it?

Math game: How to make a square out of a rectangular piece of paper for square paper-cutting?

Use the rectangular paper ABCD cut from the above question to align one of the short sides BC with the long side CD and fold it obliquely into a broken line. The point where the vertex of angle B falls on the edge of CD is marked as F, and the point where the dotted line intersects with the edge of BA is marked as E .. Then the paper is folded along E and F and unfolded. BEFc is a square. Every corner in this picture is a right angle, and each side is equal in length.

Now, cross the vertices of two diagonal corners of the square and fold out two diagonal corners. At first glance, these two diagonals intersect at right angles and are equally divided, and the intersection point is the center of the square. Look again, each diagonal divides the square into two triangles that can be superimposed together. The six vertices are all on the four vertices of a square, and they are all right isosceles triangles. Look again, two diagonal lines divide the square into four right-angled isosceles triangles that can be superimposed, and their common vertex is the center of the square.

Now, fold the two opposite sides of the square in half to get two broken lines. These two dotted lines, passing through the center of the square, bisect each other, perpendicular to a pair of opposite sides of the square, bisect these two sides, parallel to the other pair of opposite sides, and divide the square into two rectangles that can be folded and overlapped. These two rectangles consist of four overlapping squares, and each rectangle consists of a large right-angled isosceles triangle and two small right-angled isosceles triangles.

If you fold a small inscribed square with a smaller inscribed square in this square, as shown in the figure, there will be more similar changes.

Math game: rectangular paper-cutting. How to cut a rectangle with a knife?

Put the paper on the table, fold the paper on the edge near one edge E, and cut a small piece of paper along the folding line with a knife to get the straight edge EAD. Then, in the ED direction, a segment of EA and AD overlap together, thus reaching the dotted line AB.

Convert DC and BC in the same way. Cut off the extra parts, and ABCD is a rectangle.

Math game: a teenager selling eggs. A teenager pushes a basket of eggs in a car to sell. On the way, a walking tractor hit the car, the basket fell to the ground and all the eggs were broken. The driver wanted to pay him back and asked him how many eggs he had. "I don't know." The boy said, "I only remember that when I moved one by one, there was only one left." When I picked up three, four, five and six eggs, there was one left. When I press seven, there is no one left. Please count how many eggs there are. "

The driver thought, this is asking for a number: it can be divisible by seven, by two, three, four, five and six, and there is a remainder that is one. The smallest number divisible by two, three, four, five and six is the least common multiple of these numbers, which is sixty. In other words, the required number is: a number divisible by seven and greater than a multiple of sixty by one.

This figure can be obtained through continuous trial and error:

60 ÷ 7 = 8, leaving 4;

2× 60 ÷ 7 = 17, and the remainder is1;

3× 60 ÷ 7 = 25, and the remainder is 5;

4× 60 ÷ 7 = 34, and the remainder is 2;

5× 60 ÷ 7 = 42, and the remaining 6.

5×60+ 1÷7=43。

Ah, there are at least 5× 60+ 1 = 30 1 in the juvenile basket. Think about why the driver's algorithm is right

Math game: Aunt Mushroom Picking took four children to the Woods to pick mushrooms. In the Woods,

They split up and looked everywhere. Half an hour later, my aunt sat under the tree to have a rest. She counted the mushrooms in the basket, and she chose 45. Soon, all the children ran to her with empty baskets and no mushrooms.

"Aunt," a child begged, "give me a mushroom. If the basket is not empty, a lot of mushrooms will be picked. "

"Give me one, too."

"I want it, too."

Aunt gave all the mushrooms she picked to the children. After that, everyone went to choose separately. The first child found two mushrooms. The second child lost two mushrooms; The third child picked so many mushrooms that his aunt gave him; But the fourth child lost half of what his aunt gave him. When the children returned to kindergarten, they counted their mushrooms. Hey, what a coincidence! It turns out that everyone has the same number of mushrooms in his basket. Excuse me: How many mushrooms does each child get from his aunt? How many mushrooms did everyone have when they returned to kindergarten?

On second thought, menstruation gave Lao San the least mushrooms because he picked half of them himself. For convenience, suppose aunt gave the third child a handful of mushrooms. He picked as many mushrooms as his aunt gave him, and the third child brought back two handfuls of mushrooms. The fourth child brought back as many mushrooms as the three children, two of them. But he lost half of it on the way, so his aunt gave him four mushrooms.

The first child brought back two handfuls of mushrooms, and he picked two by himself. Actually, his aunt gave him two handfuls of mushrooms.

The second child also brought back two handfuls of mushrooms, but he lost two on the way. In other words, his aunt gave him two handfuls and two more mushrooms.

Aunt gave the child one plus four plus two plus two mushrooms, one * * * nine, two of which were missing two, and the other two were more than two, which just offset. It is known that Aunt Yi * * * picked 45 mushrooms, each with 45 ÷ 9 = 5 mushrooms. Well, the following questions are easy to answer.

Math game: a square city has a square city, and sixteen sentries are needed to stand guard on the wall. The security squad leader is arranged according to five people on each side.

The platoon leader is here. He was dissatisfied with the arrangement of the sentry and ordered six people to be deployed on each side. After the platoon leader left, the company commander came. He made a patrol and ordered the deployment of seven men on each side. According to the orders of the platoon leader and company commander, how should sixteen sentries be arranged?

Math game: Two teenagers selling apples sell big apples in the market. One wants two apples for fifty cents, and the other wants three apples for one yuan. There are thirty apples in each basket. The first teenager can sell for seven dollars and fifty cents, and the second teenager can sell for ten dollars. In order to be friendly and easy to buy and sell, they agreed to sell apples for two people together, one yuan and fifty cents. After the sale, they were surprised to find that they sold 18 yuan, which was 50 cents more than they could have sold. That's right. Why is there an extra fifty cents? Who should get the money? When two teenagers were trying to figure out what was going on, they were heard by two other teenagers selling apples. They thought that two people could make more money by selling together and decided to sell it this way.

The two teenagers also have thirty apples each. One wants two apples for one yuan, which can be sold for fifteen yuan; The other one costs one yuan for three apples, which can be sold for ten yuan, and one * * * can be sold for twenty-five yuan. But after the five dollars were sold out, they were also surprised to find that the total price was only 24 yuan, which was one yuan less than that of two people selling separately.

In the same way, the result is that one sells 50 cents more and the other sells one yuan less. This is really weird. In fact, when two teenagers sell apples together, it is no longer their own price. They won't be surprised if they consider this. Ok, now let's take the selling method of two teenagers as an example to see how they sold one yuan less:

If the apples are sold separately, the first teenager wants two apples to sell for one yuan, that is, one apple sells 1/2 yuan; Another teenager is three apples for one yuan, that is, one apple 1/3 yuan. When they put apples together and sell them at two yuan for every five apples, the price of each apple becomes 2/5 yuan. That is to say, all the apples of the first teenager are not sold at the price of 1/2 yuan, but at the price of 2/5 yuan, and each apple is missing110 yuan (1/2-2/5 =1/kloc-. Another teenager's apples are not sold by 1/3 yuan, but by 2/5 yuan, so each apple sells115 yuan (2/5-1/3 =), and one * * is thirty apples, more than * *. Two are almost the same, of course, one yuan less than those sold separately.

Now, it is easy to understand why the first two teenagers sold 50 cents more.

Math game with hands and brains: how to connect the following points with four continuous straight lines to make a 9-point stroke?

Please note that when drawing a line, the pen can't stop or break. )

. . .

. . .

. . .

A math game with hands and brains: arranging chairs skillfully

As the picture shows, someone invited 14 guests to eat at a large hexagonal table, even himself was 15. He wants to sit three people on each side, but he doesn't know how to put the chairs. Clever, can you help him

A hands-on math game: divide the cake into seven pieces, each with a flower.

Mathematical game with hands and brains: the numbers on the dial divide the dial of the watch into three parts with two straight lines, so that the sum of the numbers in each part is equal. How should I divide it?

If it is divided into six parts and the sum of the numbers is equal, how to divide it?

Interesting Mathematics in Primary School: Daisy Game

It was the midsummer of 1865, and I followed a tour group in the Swiss Alps from Altdorf to Fleren. On the way, we met a little girl from the countryside who was collecting daisies. In order to tease the child, I taught her how to predict the future marriage by picking petals. Who will her husband be: rich, poor, beggar, or thief bone? She said that girls in rural areas have long understood this kind of game, but the rules of the game are slightly different: the game is played by two people, and each person takes turns picking a petal or two adjacent petals freely. The game goes on like this until the last petal is picked by one person, and this person is the winner. Leave the opponent a bare backbone called "one-man army", and the opponent is the loser of the game.

To our surprise, Gretchen, a little girl who is unlikely to be over 10, actually made our whole tour group very depressed. No matter who picks first, she always wins every game. On the way back to Lucerne, I never understood the mystery. Being teased by the whole tour group, I made up my mind to study the game.

By the way, a few years later, I returned to Altdorf and revisited my old place. I hope to see Gretchen grow into a beautiful girl with extraordinary mathematical talent, which will undoubtedly add romance to this story. I will also feel extremely happy for this.

There is no doubt that I must have met her, because all the women in the village have left home and are busy planting autumn crops. They are all mature and plump, and they all look the same. So I saw a friend I had seen before in a trance. She is pulling a plow with an ox and plowing the field under the command of her noble husband.

The picture below shows a daisy with 13 petals. Two people can take turns to make a small mark on the petals, one for each petal, or one for two adjacent petals. Whoever marks the last mark is the winner, and the other side has to accept the "one-man army." Can our fans tell us who is sure to win the game, first or last? What strategy should he adopt to win?

Answer:

As long as the latecomers divide the petals into two equal groups, they will surely win the daisy game.

For example, if the first runner picks one petal, the last runner can pick two opposite petals, leaving two groups with five petals each; If the first runner picks two petals and the last runner picks the opposite petal, the result is the same as above. After doing this, the latecomers only need to "imitate" the actions of the pioneers. For example, if the first runner takes two petals and leaves a combination of 2- 1 in one group, the last runner can also take the corresponding two petals and leave a combination of 2- 1 in the other group. In this way, he will definitely take the last step, so he will fail.

Interesting math game: Can you get the admission ticket?

The whole class got a ticket for the football match, and both soldiers and ghosts scrambled to go. Teacher Wang hesitated. Who should he give it to?

The whole class got a ticket for the football match, and both soldiers and ghosts scrambled to go. Teacher Wang hesitated. Who should he give it to?

There are 54 math books on the desk, so Miss Wang puts this admission ticket in the bottom math book.

Teacher Wang said, "Here are 54 math books. You two take turns taking books, and you can take 1 to 5 at a time. Whoever gets the last one will be given the voucher inside. "

Lingling is really clever. He let the soldiers take it first, and he got the ticket firmly. Children, do you have the ability of Ling Lin?

Lingling is really smart. He thinks: To get the last book, you must force the soldiers to take the sixth from the bottom, the sixth from the bottom, and the12 from the bottom; In order to get the tickets, the opponent must be the sixth from the bottom, 12, 18, 24, 30, 36, 42, 48 and 54 books. In this way, as long as Lingling lets the soldiers take it first, when he takes 1, 2, 3, 4 and 5 copies respectively, he can take 5, 4, 3, 2 and 1 copies respectively, and he can get this admission ticket.

Hope to adopt, thank you! ! !