PAT Advanced 1069 The Black Hole of Numbers (20) [数学问题-简单数学]
题目 For any 4-digit integer except the ones with all the digits being the same, if we sort the digits in nonincreasing order first, and then in non-decreasing order, a new number can be obtained by taking the second number from the first one. Repeat in this manner we will soon end up at the number 6174 — the “black hole” of 4-digit numbers. This number is named Kaprekar Constant. For example, start from 6767, we’ll get: 7766 – 6677 = 1089 9810 – 0189 = 9621 9621 – 1269 = 8352 8532 – 2358 = 6174 7641 – 1467 = 6174 … … Given any 4-digit number, you are supposed to illustrate the way it gets into