数学黑洞6174

已知：一个任意的四位正整数。将数字重新组合成一个最大的数和最小的数相减，重复这个过程，最多七步必得6174。即：7641-1467=6174。将永远出不来。

求证：所有四位数数字（全相同的除外），均能得到6174。输出掉进黑洞的步数-6174 known mathematical black hole: an arbitrary four positive integer. The re-assembled into a digital number and the maximum number of minimum subtraction process is repeated up to seven steps must 6174. That :7641-1467 = 6174. Will never get out. Prove: All four-digit number (except identical), and can get 6174. Output fell into the black hole of the number of steps