How many even four digit numbers can be formed by the 10 numbers of 0 ~ ~ 9 The calculation steps are given

Answer: 2296 please take a close look at the following problem-solving process
Thousand bits 1,2,..., 9
Hundreds 0,1,2,..., 9
Ten digits 0,1,2,..., 9
Bits 0,2,4,6,8
（1）
If one bit is 0
There are nine possibilities for a thousand
There are eight possibilities to get rid of the zero and the thousand
There are seven possibilities to get rid of 0, 1000 and 100
Total 1 * 9 * 8 * 7 = 504
（2）
If the one digit is 2
There are eight possibilities for a thousand
There are eight possibilities to get rid of the two and the thousand
There are seven possibilities to get rid of 2, 1000 and 100 in ten
Total 1 * 8 * 8 * 7 = 448
（3）
There are 448 possibilities in the same (2) principle
Comprehensive (1) (2) (3) a total of
504 + 4*448
=2296 4-digit numbers with different 4-digit numbers

Use the five numbers of 0, 1, 2, 3 and 4 to form many four digit numbers without repetition. What is the sum of all even numbers in these four digit numbers?

(1) In the case of 2 bits, there are 3 × 2 = 6 numbers with thousand bits as 1, 3 × 2 = 6 numbers with hundred bits as 1, 3 × 2 = 6 numbers with ten bits as 1, and the sum is 1 × (6000 + 600 + 60) = 6660. Similarly, for the same number of 3 and 4, the number of 2 bits is 4 × 3 × 2 = 24, and the sum of all even numbers is (1 + 3 + 4) × 6660 + 24 × 2 = 8 × 6660 + 24 × 2; (2) the number of 4 bits is 4 The sum of four digits is: (1 + 2 + 3) × 6660 + 4 × 24 = 6 × 6660 + 4 × 24; (3) the sum of four digits is: (1 + 2 + 3 + 4) × 6660 = 10 × 6660; the sum of all even numbers in these four digits is: (8 + 6 + 10) × 6660 + (2 + 4) × 24, = 24 × 6666, = 159984; a: the sum of all even numbers in these four digits is 1599984

Use 1.2.3.4. These four numbers can form even numbers of four digits without repetition

12:
one thousand two hundred and thirty-four
two thousand one hundred and thirty-four
one thousand three hundred and twenty-four
three thousand one hundred and twenty-four
two thousand three hundred and fourteen
three thousand two hundred and fourteen
one thousand three hundred and forty-two
three thousand one hundred and forty-two
one thousand four hundred and thirty-two
four thousand one hundred and thirty-two
three thousand four hundred and twelve
four thousand three hundred and twelve

What is the even number in the five digit number of the non repeated number composed of 1,2,3,4,5?

Consider the last digit first
1. When the end is 2, the first four numbers have 4 * 3 * 2 * 1 = 24 choices
2. When the end is 4, the first four numbers have 4 * 3 * 2 * 1 = 24 choices
The total number is 5 * 4 * 3 * 2 * 1 = 100
So even 48 / 100 = 6 / 25

Use 1,2,3,4,5 to form a three digit number without repetition. How many even numbers are there

2. 4 ends with an even number
At the end of 2, 1, 3, 4 and 5 are combined with 2 bits, and there are 12 kinds of 3 * 4
At the end of 4, 1, 2, 3 and 5 are combined with 2 bits, and there are 3 * 4 = 12 kinds
There are 24

How many (1) four digits can be made up of numbers 0, 1, 2, 3 and 4? (2) Four even numbers? (3) Four digits without repeating numbers? (4) Four even numbers without repeating numbers?

(1) ∵ the highest order of this four digit number can not be 0, so there are four ways to choose the highest order (i.e. choose any number from 1 to 4), and the rest of you can choose from the five numbers from 0 to 4, so there are a total of 4 × 5 × 5 × 5 = 500 four digits; (2) even numbers can also be obtained by similar methods, there are 4 × 5 × 5 × 3 = 300

How many digits can be made up of 1,2,3,4,5? 1. Five digits without repetition. 2. Four even digits without repetition

120,48

If the product of three adjacent even numbers is four digits and the last digit is 8, find the three even numbers

If the product of three adjacent even numbers is 4-digit * 8, find three adjacent even numbers

The product is a four digit number, and its last digit is 8. Obviously, the last digit of these three numbers can only be 2, 4 and 6. Because the product is a four digit number, only 12, 14 and 16 meet the requirements
Method 2
（x+2)x(x-2)=x^3-4x
The even number of digits 0, 2, 4, 6 and 8 are substituted into
It is found that only when the single digit is 4, the single digit of x ^ 3-4x is 8
So the single digits of the three even numbers are 2, 4 and 6 respectively
However, the root of the third power of 10000 is 21.5, less than 21.5, and the end number is 2,4,6. At the same time, the even number of 4-digit product is only 12,14,16

The product of three adjacent even numbers is a four digit number, in which the number in thousand is 4 and the number in one digit is 2. What are the three numbers?

The bits of the three even numbers can only be 2, 4, 6 or 4, 6, 8, because if there is a 0, the number of the product will not be 2
It is further verified that the last position of 2 × 4 × 6 is not the same as the title, so the individual position must be 4, 6 and 8
Because the product of these three even numbers is about equal to the cube of the middle number
So the middle number must be two digits, and the ten digits are smaller
One by one, the results can only be 14, 16, 18

How many even four digit numbers can be formed by the 10 numbers of 0 ~ ~ 9 The calculation steps are given