Thoughts, no. 20
Take any four-digit number whose digits aren’t all the same. Arrange its digits from largest to smallest, then smallest to largest, and subtract. Do it again with the answer, and again. Within seven steps you will land on 6174, and stay there, because 7641 minus 1467 is 6174. This year does it in six: 2026, 5994, 5355, 1998, 8082, 8532, 6174. A schoolteacher named D. R. Kaprekar found this in 1949, and for years hardly anyone took his little discoveries seriously. I like it because it isn’t useful for anything. It’s just a place every four-digit number is secretly walking toward.
Written at the house on .