A and B play a math game with the following rules

A and B play a math game, the rules are as follows: they start with A and cross out one of the numbers in the nine-digit 123456789 in turn, and each crosses out three digits to leave a three-digit number, if the three-digit number is an even number or a multiple of 25, then A will win, otherwise B will win. Who will emerge victorious?

B wins. B crosses out 7 and 9 the first two times. Conclusion: Plan first and win.

Two bases: A: 3, 4, 5 will win, B: 8 will lose.

Draw 678, one at both ends has 5 left, one has 12 left, and 5 can only be stroked once no matter how you draw it.

1) If the opponent first rows 12 inside:

12No matter how the opponent rows first, you can let the opponent draw the last stroke of the 12 with your own hand (both you and your opponent want the opponent to make the last stroke).

Method: If the opponent has 0 left at one end and 9 left at the other end, then you can draw 3 of the 9 (2 at one end, 4 at one end or 1 at one end, 5 at one end, and the opponent can only draw 4 or 5).

In the same way, the opponent keeps 1 or 2 at one end, 7 or 8 at the other, and your own draw (7 or 8) leaves no more than 5 heads at one end and no more than 2 heads remaining.

If the opponent leaves 3 at one end and 6 at the other end, then you choose the middle of the 6, and the opponent can only draw 3 in the other head.

If the opponent leaves 4 at one end and 5 at the other, then draw at will, and the opponent will draw 12 and the last stroke.

2) If the opponent draws 5 first:

No matter how the opponent rows in the 12, you can make the last stroke of the 12 miles by yourself (both you and the opponent want to draw the last stroke). Method: Party B draws three and leaves 8 at one end, and 1 at one end.

Let the opponent draw 8 first, no matter how you row, the opponent loses (based on B).

12 These two numbers can be ignored; Whether it is deleted or not, it is a waste of an opportunity for both sides.

A wants to win with the numbers 4, 5, 6, 8

B wants to win with the numbers 3, 5, 7, 9

But only by occupying the last number will there be an advantage;

A wants to win first draw 9, 7 and 3;

B wants to win first draw 8, 6, 4;

After two rounds, it becomes 12345;

A draws casually, and B changes to win.

The result is that B wins;

Hope to be !!

This question is a bit weird, does the question mean to find a way for them to draw numbers, or to prove that A will always lose? If I am A, the first 3 times crossed out 1 3 5, B has 2 4 6 8 left, how can A win? Unless A crosses 2 4 6 the first 3 times, and B crosses out 8 last time to win, then A is a fool and does not explain.

The title has been changed. This is easy to say, because A needs an even number or a multiple of 5 to win, so the remaining 3-digit single digit is OK to be even or 5.

First of all, A crosses out 7,9, then the rest is 1234568, then B in order not to let A win, first of all, he has to choose to cross out the remaining numbers of 2,4,6,8. So what numbers does B cross out? We see that the last two digits are 6,8, then B must cross out 6,8, otherwise cross out other numbers, the 3 digits born must be 6, 8 is a single digit 3 digits, A wins.

After B crosses out 6,8, A has already crossed out 7,9, and the rest is 12345, so A only needs to cross out 3, and the remaining 1245 B crosses out no matter which one is crossed, A wins.

A first says, 1, 2, and then no matter what B says, the number of numbers he says plus the number of numbers B says is 4, so the last numbers A says are: 2, 6, 10, 14, 18, 22, 26, 30. It's not what A hears, B is a variable, what he hears is not necessarily the same, and this type of question is basically who wins first.

Imagine that if the remaining number of numbers after Party A counts is that Party B can count to 30 once (+1 +2 +3), then the last number of numbers that Party A counts should be between 27 and 29, and A can +1 2 3 at a time, let B count to a before A, a + 1 = 27, a + 3 = 29, and a = 26.

Form: Concatenate equal formulas (or numbers represented by letters) by "=".

Equations are divided into equations with unknowns and equations without unknowns.

For example: x+1=3 - the equation with unknowns;

2+1=3 – the equation without unknowns.

It should be noted that some equations with unknowns have no solution, but they are still equations, for example: x+1=x - x has no solution.

Summary. Hello, first count the strategy that must win. Count 1 first, and then account for the key numbers of 5, 9, 13, and 17 in turn, and you can grab 21.

3.The rules of the game for A and B to compete for small flowers are: two people take turns to count, at least one at a time (

That's the ** question I sent, how to calculate it with an equation, explain the problem after adding, and how about the text.

Hello, first count the strategy that must win. Count 1 first, and then account for the key numbers of 5, 9, 13, and 17 in turn, and you can grab 21.

Teacher, I don't understand what this means, can you please explain it clearly?

Hello, this game looks like this. Whoever counts the difference to 21 first and gets the little red flower, whoever changes his spine wins. Divide the 21-point nucleus into 5 groups, each in a group of 4, so that there is 1 left. As long as you make sure to get the last 1, you win.

This game is all about the key numbers you have to get 5, 9, 13, 17. I'll give you an example, if you take it first, you will win first, take 1 first, and the opponent will take up to 3, so that you can get up to 4 in the wheel cavity base. If you take 2 or 3 on the opposite side, you take 5, and if you take 4 on the opposite side, you take it too.

It's the same later, no matter how many others take, you have to take the number 9 13 17, and the circle is so bad that in the end, the 21st number must be taken by you.

If you take it later, you can't get the numbers 5 9 13 17 by someone else, or you will lose.

What about people. You're running out of time, so I can talk to you about it.

If you calculate by formula, you can write 21 divided by 4 to equal 5 and remainder 1

Whether the opponent takes 2 or 3 or 4, you take 5. In the same way, whether the opponent takes 6 or 7 or 8, you take the 9th, and then in the same way, whether the opponent takes 10 or 11 or 12, you take 13, and then take 17, and in the end, you take 21, and you win.

After taking and ensuring that the sum of the number of matches received by the two people in each round is 3, you can win.

The idea of solving this problem is: let the other party take it first, if the other party takes 1, take 2 by yourself; The opponent takes 2 sticks, and they take 1 stick, ensuring that the total number of matches taken by two people in a round is 3, so that you can ensure that you can sell Zen 15 3 3 3 3 3 3 (root) in the end, then at this time, no matter whether the opponent takes 1 or 2, you can take yourself to the end, and you can win.

When doing this or similar question, you can use the method of backwards, based on the assumption that I got the 15th match, and then you can get the correct answer.

<> draw a treemap according to the meaning of the topic, and then find all the possible outcomes and their "mind" from the treemap, and then use the probability formula to solve the answer:

Draw a tree-like diagram to get:

There are a total of 16 possible outcomes, and m and n satisfy <>

There are 10 situations, and the probability of their "heart" is: <>

Let the number on the hundredth digit be x, the digit on the ten-digit number as y, and the single-digit number as z, and the three-digit number is 100x+10y+z

1）2x2)2x+5

3)(2x+5)*5

4)(2x+5)*5+y

5)[(2x+5)*5+y]*10+z

10x+25+y]*10+z

100x+10y+z+250=three-digit 250, that is, he unconsciously asks you to put the number on the hundred-digit number sincerity 100, the number on the ten-digit number multiplied by 10, and then add them to the single digit, of course, and subtract the extra number (250) in the process to make a spring judgment.

250,What an ironic question. =

Solution: Just subtract 100 from the three digits of Jian Qingbi that you said

Reason: Let the number on the hundred digit be a, the number on the ten difference is b, and the number on the single digit is c, then the three-digit number obtained by B according to the step is 10 [2(5a+5)+b]+c, which is simplified to 100a+10b+c+100, and subtracting 100 is the original three-digit number

a
、-9

b c, -2, -3).

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A: If you draw -10, -9, 10 will definitely win. B: If you draw -10, 9, 10, you will definitely lose. c：-6，-1，1；-3，-2，1

Solution: (1) All possible outcomes of the guess the number game are shown in the table below

2) As can be seen from the table above, the total number of all possible outcomes of the event is 36, and the total number of outcomes of the "Mind and Soul" is 16, so the probability is 16 36 = 4 9

A says m-n=0 so m=n

B says a is in the first tremor quadrant so m,n are positive integers.

C says that the absolute value of m is judged to be = 2, so the coordinates of m = 2 or m = -2 (taken by Sheqixu) are (2, 2).

The coordinates of a are (2,2)! It's easy!