Find out the reason for the formation of digital black holes, what is digital black holes

The number black hole refers to the fact that some numbers get a circular or definite answer after a certain operation, such as the black hole number 6174: choose a four-digit number at random, such as 1628, first arrange the four numbers from large to small to get 8621, and then arrange the four numbers of the original number 1628 from small to large to get 1268, and use the large one to decrease: 8621-1268 = 7353.

Repeat according to the above method, arrange 7353 from large to small, get 7533, arrange from small to large to get 3357, and decrease greatly: 7533-3357 = 4176, repeat 4176 again, get 7641-1467 = 6174. So 6174 is a black hole number.

Take any number, and write down the number of even numbers it contains in turn, and the sum of the odd numbers and these two numbers will give a positive integer. For this new number, the even number and the odd number are combined with the sum to form another positive integer, and so on, and the number 123 will inevitably stay in the end. Example:

Given numbers 14741029 First calculation result 448 Second calculation result 303 Third calculation result 123 Multiply the sum of the three digits by 2 to obtain the number as the hundredth and tenth digits of the three digits; The sum of the ten digits of the original number and the single digit number (if two digits are obtained, the sum of the numbers is obtained by adding the numbers) as the single digit of the new three digits. After that, repeat the process for the three digits of the reorganization, and you will see that there must be a number of fall traps.

First of all, it can be noticed that obviously any number can get a three-digit number after a finite step transformation Secondly, for the obtained three-digit number, it may be 3 odd 2 odd 1 even 1 odd 2 even 3 even After changing according to the given way, you will find that after no more than two steps, it will definitely become 123, and 123 will still change again 123 So it enters the loop like this.

Digital black hole, also known as a certain operation, is generally limited to a certain integer, and the result will inevitably fall into a point or several points after repeated iterations is called a digital black hole.

Black holes are originally an astronomical concept that represents a celestial body whose gravitational field is so strong that not even light can escape.

The number of black holes, also known as trap numbers, is an integer with peculiar conversion characteristics, and any integer whose numbers are not exactly the same, after a finite rearrangement and difference operation, will always get a certain number or numbers, and these numbers are the number of black holes, and the number rearranged is rearranged to a large number minus a decimal number.

The value of a black hole is set as an arbitrary string of numbers, counting the even, odd, and total number of digits in the number.

Caprekar Black Hole:

1. Three-digit black hole 495

As long as you enter a three-digit number, the number of numbers, tens, and hundreds is not the same, such as 111,222, etc. Then you rearrange the three digits of the three-digit number according to their size to get the largest and smallest numbers, subtract the two to get a new number, and then rearrange them in the same way as above, and then subtract them, and you always get the number 495.

For example, enter 352 to arrange the largest digit 532, the smallest number to 235, subtract to get 297, then arrange 972 and 279, subtract to get 693, then arrange 963 and 369, subtract to get 594, and finally arrange 954 and 459, subtract to get 495.

2. Four-digit black hole 6174

Arrange the four digits of a four-digit number from smallest to largest to form a new number, and arrange them from large to smallest to form a new number, subtract the two numbers, and then repeat this step, as long as the four digits of the four-digit number are not repeated, the number will eventually become 6174.

For example, 3109, 9310 minus 0139 equals 9171, 9711 minus 1179 equals 8532, 8532 minus 2358 equals 6174, and the number 6174 will also become 6174, and 7641 minus 1467 equals 6174.

Generally, the situation that starts from some integers and inevitably falls into one point or several points after repeated iterations is called a digital black hole.

Four-digit black hole 6174

Arrange the four digits of a four-digit number from smallest to largest to form a new number, and arrange them from large to smallest to form a new number, subtract the two numbers, and then repeat this step, as long as the four digits of the four-digit number are not repeated, the number will eventually become 6174.

For example, 3109,9310 - 0139 = 9171,9711 - 1179 = 8532,8532 - 2358 = 6174. And the number 6174 will also become 6174, 7641 - 1467 = 6174.

Take any four-digit number, as long as the four numbers are not identical, they are arranged in decreasing order to form the largest number as the subtracted number; Arranged in ascending order of numbers, the smallest number is formed as a subtraction, and the difference will be 6174; If it is not 6174, then subtract according to the above method, and at most 10 steps will inevitably get 6174.

If you take the four-digit number 5679, the above method is used to calculate as follows:

123 in math is as mundane and simple as ABC in English. However, this simplest number can be observed in the following order of operation.

The value of the black hole: set an arbitrary string of numbers, count the even number, the odd number, and the total number of digits in the number, for example: 1234567890, even:

Count the even number of the number, in this case 2, 4, 6, 8, 0, for a total of 5.

Odd: Count the odd number of numbers in that number, in this case 1, 3, 5, 7, 9, for a total of 5.

Total: Count the total number of numbers for that number, in this case 10.

New number: Sort the answers in the order of "even-odd-total", and the new number is: 5510.

Repeat: Repeat the new number 5510 according to the above algorithm to obtain the new number: 134.

Repeat: Repeat the new number 134 according to the above algorithm to get the new number: 123.

Conclusion: Logarithmic 1234567890, according to the above algorithm, the final result of 123 must be obtained, we can use the computer to write a program, test that any number will be 123 after a finite number of repetitions. In other words, the end result of any number cannot escape the 123 black hole.

The number of black holes, also known as trap numbers, has peculiar conversion characteristics, integers are all the same integers, and after finite rearrangement and difference operation, there will always be some or some numbers, and some numbers are black hole numbers, that is, the number of the number is rearranged to a large number minus the decimal number of the number Black hole is originally a concept in astronomy, indicating such a celestial body: its gravitational field is so strong that even light cannot escape.