Once we hit 6174 the sequence starts repeating, as the result of applying this “biggest digit-arrangement minus smallest digit-arrangement” operation to 6174, is 6174 itself. Or in maths parlance: 6174 is a fixed point of this operation. Now here’s the kicker: as long as the starting number is not a single repeated digit, we can start from any 4-digit number and the sequence will always reach 6174