Out of all the four digits, the sum of the digits is 10 and how many four digits there are

There are 219 in total.

The combination of three numbers is 6 (all combinations containing two zeros are 6, c(2,1)*p(3,3) 2=6), a total of 9, a total of 18, a total of 18, a total of 18, a total of 4, a total of 12, a total of 12, a total of 12, a total of 12, a total of 24, a total of 4, a total of 6, a total of 9, a total of 18, a total of 9, a total of 4, a total of 6, a total of 6, a total of 6, a total of 3.

There are 219 in total.

Because there may be 0s in hundreds, tens, and single digits, this question can be equated to how many four-digit numbers without zeros are there when the sum of the four digits is 13.

It can be understood as dividing 13 1's into four groups, i.e., c(12,3)=220. However, it cannot be 10 in the thousand digits (hundreds, tens, and units can be 10 because they have been added by 1), so this exception should be subtracted. So the answer is 219.

c(3,7)-c(2,6)=35-15=20 each plus 1, the sum of the four digits is 8, divided into four parts, 7 intervals take 3 and at least intervals of 1, then there is c(3,7).

The case where the first part is 1 is removed, because the first place is 0 after subtracting 1, this case is 7 points and 3 points, and the interval between 6 takes 2 and at least intervals of 1, then there is c(2,6).

The obtained number is subtracted by one for each case, which corresponds to one to one, and the result is 20 when the two cases are subtracted

If the number on each digit of a four-digit number is different, and the sum of the digits on each digit is 14, how many of these numbers can be written? “

Arabic numerals

The first thing to do is to determine the combination of four different Arabic numerals that add up to 14.

Slag and withering ; Sheltered.

When the selected Arabic number such as the hole has 0, the thousand digit can choose 3 kinds of numbers (0 cannot be selected), the hundred digit can choose 3 kinds of numbers, the ten digit 2 kinds, and the single digit 1 kind, that is, 3x3x2x1 = 18 kinds. The above 8 combinations have a total of 18x8=144 species;

For the above 5 combinations, 4 kinds of numbers can be selected for thousands, 3 kinds can be selected for hundreds, 2 kinds for 10 places, and 1 type for each person, that is, 4x3x2x1=24 kinds.

These 5 combinations are 24x5=120 in total.

A total of 144 + 120 = 264 species.

This is enumerated.

Let all the digits be 0, the simplest is 1111;

If there is 1 bit of 0, if the single bit is 0, there are 2110, 1210, 1120;The ten springs are 0,1102,1201,2101;The hundred digits are 0, 1012, 1021, 2011If the thousand digit is 0, it is not a four-digit number.

If there are 2 digits of 0, the single digit of ten is 0, 1300, 3100, 2200, the single digit of 100 is Sui rent 0, 1030, 3010, 2020, and the 100th digit is 0, 1003, 3001, 2002

If there are 3 digits with 0,4000, there are 20 numbers to guess.

According to the title, the sum of a two-digit, single-digit and ten-digit number is 4, which is broken down into 1

Then the two-digit numbers can be 13, 31, 22, 40

Hello, such a two-digit number can be 40, 31, 13, 22

Multiply the fraction by an integer.

2/1x8=16

5/8x4=5/2

6/5x5=6

8/7x7=8

Fractions multiplied by fractions.

1/2x6/5=3/5

1/7x1/8=1/56

8/9x2/7=16/63

1/22x22/4=1/4

Fractions divided by fractions.

Multiply the fraction by an integer.

2/1x8=16

5/8x4=5/2

6/5x5=6

8/7x7=8

Fractions multiplied by fractions.

1/2x6/5=3/5

1/7x1/8=1/56

8/9x2/7=18/63

1/22x22/4=1/4

Fractions divided by fractions.

Combining four 1s has only one number, 1111

Combine the four numbers of 2110, respectively

Combine the four numbers of 3001, respectively

Combine the four numbers of 2002, respectively

There are a total of 6 combinations of numbers in the three leaky chains (the combinations that contain two 0s are 6);

9 in total; 18 in total;

18 in total; 18 in total;

4 in total; 12 in total;

12 in total; 6 in total;

12 in total; 24 in total;

4 in total; 6 in total;

9 in total; , a total of 18 returns;

9 in total; 4 in total;

6 in total; 6 in total;

9 in total; 6 in total;

3 in total. There are 219 in total.

Summary. Hello <>

The problem that the sum of the digits on each digit of this four-digit number is 14 can actually be solved by enumeration. First of all, since the maximum number of thousands of a four-digit number can only be 9, and the maximum number of other three digits is 9*3=27, the sum of the digits of this four-digit number cannot exceed 27+9=36. So, we just need to enumerate from 1000 to 9999 and find the number where the sum of the digits equals 14.

After calculation, we can get that this four-digit number is 4103.

A four-digit number, and the sum of the digits on each digit is 14

Hello <>

The problem that the sum of the digits on each digit of this four-digit number is 14 can actually be solved by enumeration. First of all, since the maximum number of thousands of a four-digit number can only be 9, and the maximum number of other three digits is 9*3=27, the sum of the digits of this four-digit number cannot exceed 27+9=36. Therefore, we only need to enumerate from 1000 to 9999 and find the number where the sum of all the numbers is equal to 14.

After calculation, we can get that the four-digit number of cavity is 4103.

Another 1For similar problems, if there are more digits, then the enumeration method does not apply. At this point, we can use mathematical methods, such as using the knowledge of combinatorial mathematics to solve the problem.

2.In addition, in the process of solving this problem, we can also find that the problem of the sum of the numbers being fixed can be transformed into a ball loading problem. For example, for this problem, we can put 14 small balls into 4 boxes, where the first box must put 1 ball or more, the second box of liquid potatoes must put 0 balls and above, the third box must put 0 balls and above, and the fourth box must put 0 balls and above, so that you can get the eligible four digits.

In short, there are many ways to solve this problem, and you need to choose the appropriate method according to the specific situation.

Problem solving ideas: According to the knowledge of numbers, it can be known that the smaller the number on the high position of a number, the smaller the value of this number, and the larger the number on the high position, the greater the value of this number The sum of the numbers on each digit of this number is 10, if you want to make this number small, 1+9=10, you can make the thousand digit of this number 1, the single digit 9, and the hundred and ten digits 0, that is, 1009; Answer accordingly

1+9+0+0=10, according to digital knowledge, the minimum number is 1009

So the answer is: 1009 ,6,

A: There are four digits: 143,246,349

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Let the ten digits be a and the single digit be b

Then the thousand digit is 3a, and the hundred digit is b+1

a+b+3a+b+1=15

4a+2b=14

Get: b = 7-2a

There are 3 sets of solutions:

When a=1, b=5, this number is 3615

When a=2 and b=3, this number is 6423

When a=3 and b=1, this number is 9231

These three numbers abc, then.

b=3/4c

a+b-1=c

100c+10b+a-(100a+10b+c)=495, that is, 99c-99a=495

The solution is a=3b=6

c=8These three numbers are 368

1790 Because the hundred is two times smaller than the ten, and six times greater than the thousand, and the thousand is definitely not 0, so the hundred is 7, so this number is 1790, understand?

If the unit is x, then the ten digits are x+1, and the hundred digits are (x+1) 4

Get ((x+1) 4+x)=x+2

The solution is x=7, so 287

Let the original single digit be x, then the ten digit is and the hundred digit is x+2

x=6, so the original three-digit number is 836

Let the hundred digit be x, then the ten digit is 2x, and the single digit is (x+4).

Because the sum of the digits on the three digits is 12, x+2x+(x+4)=12

4x+4=12

x=2 so the ten digits are 4 and the single digit is 6

So that three-digit number is 246

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There are a few possibilities.

For example, 4231

Wait a minute. A 3-digit number, the number on the ten digit is 2 larger than the number on the single digit, the number on the hundred digit is 2 times the number on the digit, if the number on the hundred digit is reversed with the number on the single digit, then the resulting 3-digit number is 495 smaller than the original 3-digit number, find the original 3-digit number.

If the single digit is x, then the number in the tenth digit is x+2 and the number in the hundred digit is 2xFrom the meaning of the title.

200x+10(x+2)+x-495=100x+10(x+2)+2x

Solution, x= is enough.

Let the ten digits be x, the hundred digits be (x+1), and the single digit be (3x-2).

by 100 (x+1) + 10x+ (3x-2) + 100 (3x-2) + 10x+ (x+1) = 1171

100x+100+10x+3x-2+300x-200+10x+x+1=1171

424x-101=1171

424x=1272

x=3, this three-digit number is 437