Two people take turns to start counting from 1, each person can only report one or two numbers each time, who first report to 30 who wins, how to report to win There is also a question. The average score of mathematics and English in the midterm exam is 93. If the average score after adding Chinese is 94, what is his Chinese score

In the first question, if you want to win, you must report the second number, and the last number must be a multiple of 3
For example, when others report 1, you report 2 or 3; when others report 1 or 2, you report 3, and so on!
To put it simply, ask others to shout first, if they shout one number, you shout two; if they shout two numbers, you shout one, no matter what, you can shout to 30!
Question 2, 94 × 3-93 × 2 = 96

Two people start counting from 1. Each person can report up to 3 numbers each time. They can report 1 number or 2 numbers each time. If anyone finally reports to 30, he will lose. If you report first, how can you give 30 to the other party?

30-1=29 …… I want to get 29
29/(1+3)=7…… 1 …… If every four numbers are in a group, there is one more number
So I have to take the extra one, and then the remaining 28 are just multiples of 4. No matter how many of the three numbers are reported by the other party, I want to make sure that two people report four numbers together to win

Arrangement and combination of multiple choice questions: now need to prepare an eight digit serial number, as follows: serial number by 4 numbers and
Permutation and combination multiple choice questions: now we need to compile an eight digit serial number, which is specified as follows: the serial number consists of four numbers and two X, one y, and one Z; two X cannot appear continuously, and Y is in front of Z; the number is selected between 1, 2, 4, and 8, which can be selected repeatedly, and the product of four numbers is 8, then the number of different serial numbers that meet the conditions is () a.12600 b.6300 c.5040 d.2520, But after I calculated, it was B

There are 20 ways to arrange YZ. When YZ is adjacent, there are five ways. When YZ is not adjacent, there are C (5,2) ways. Finally, there are C (7,2) ways to arrange X
So there are 20 * (5 + 10) * 21 = 6300

How many four digit numbers can be made up of the numbers 0, 1, 2, 3, 4 and 5, which have no repetition and can be divided by 5

There are two cases
1) A (1,) * a (5,3) = 1 * 5 * 4 * 3 = 60
2) Take one from 1,2,3,4 as the highest position, and then take two from the remaining four as the middle two,
A (1,1) * a (4,1) * a (4,2) = 1 * 4 * 4 * 3 = 48
Therefore, the total number of four digits is 60 + 48 = 108

It can be made up of 0.1.2.3.4.5___ A four digit number that has no repetition and can be divided by 5

If the last one chooses 5, the first one has 4 choices, the second one has 4 choices, and the third one has 3 choices, 48 in total
If the last one is 0, then the first one has five choices, the second one has four choices, and the third one has three choices, 60 in total
There are 108 species

Use the numbers 0, 1, 2, 3, 4 and 5 to form a four digit number without repetition. The four digits that can be divided by 3 are______ One

The sum of all the numbers is a multiple of 3, which can be divided by 3. The following are in line with the meaning of the question: first, if 0 and 3 are included, 1, 4 & nbsp; and 2 and 5 each take one, which can form c21c21c31a33; second, if 0 or 3 are not suitable for the meaning of the question; third, if 0 and 3 are not included, 1, 2, 4 and 5 can form a44, with a total of c21c21c31a33 + a44 = 96

How many four digit numbers can be made up of 0,1,2,3,4,5 which are not repeated and divisible by 3

0 + 1 + 2 + 3 + 4 + 5 = 15 can be divided by 3
So the sum of the two unselected numbers has to be divided by three
Combinations that can be removed (0,3) (1,2) (1,5) (2,4) (4,5)
So the combination of four digits is
(1,2,4,5)(0,3,4,5)(0,2,3,4)(0,1,3,5)(0,1,2,3)
The first group can be composed of four digit number 4! = 24
The number of the remaining four groups is 3 * 3 * 2 * 1 = 18
So the total number is 24 + 18 * 4 = 96

How many of the five digits of the unrepeated number composed of the six digits 0.1.2.3.4.5 are divided by three?

The sum of the numbers divisible by 3 is also a multiple of 3,
∵ 0+1+2+3+4+5=15
Only 0 or 3 less than 5 digits
(1) No 0
The five numbers are arranged in full, and a (5,5) = 120
(2) No 3,
There are four ways to arrange 0, and the other four numbers can be arranged arbitrarily,
There are 4 * a (4,4) = 4 * 24 = 96,
The number of satisfying the condition is 120 + 96 = 216

Use the numbers 1, 2, 3, 4, 5 and 6 to form the four digit sequence without repetition, from small to large?

1 is the first four digits: 1 * 5 * 4 * 3 = 60
2 is the first four digits: 1 * 5 * 4 * 3 = 60
3 is the beginning
Starting with 312, three
Starting with 314, three
3142 3145 3146, respectively
So 3145 is the 125th

Make 1, 2, 3, 4, 5 numbers without repetition, and arrange them in a sequence from large to small
(1) What is the number 43251 of this sequence
(2) What is the 96th item of this sequence?
(3) Find the sum of the items of this sequence?

Then: (1) the numbers larger than 43251 are: 4! = 24 starting with 5; 3! = 6 starting with 45; 2! = 2 starting with 435; and 24 + 6 + 2 = 32 starting with 43251