Black hole principle 6 174

Black hole 6 174 is a mysterious number. It's four digits, and the numbers on any one of them are different. Arrange these four numbers from big to small to get a new four numbers, then arrange these four numbers from small to big to get another new four numbers, and then subtract the last number from the previous one to get a new number. Repeat the above steps. No matter what the initial number is, the final number must be 6 174.

The principle of black hole 6 174 is based on the special properties of this four-digit number. First of all, if any one of the four digits is 0, then the numbers arranged from big to small and from small to big are not four digits, so they do not meet the conditions. Secondly, if the four digits of the four digits are all the same, and the two numbers arranged from the largest to the smallest and from the smallest to the largest are the same, then the result obtained after subtraction is 0, and the number obtained after the next operation is still 0, which will not change again, so it does not meet the conditions.

For the other four digits, no matter what the initial number is, it will eventually converge to 6 174. This is because in each operation, after subtracting two numbers arranged from the largest to the smallest and from the smallest to the largest, the result is a three-digit number, and the three-digit number has special properties similar to the four-digit number, and eventually converges to a fixed number, which happens to be 6 174.

The mysterious nature of black hole 6 174 has aroused many people's interest and exploration, and also stimulated people's research and thinking on mathematics.