A simple proof for a fun problem

Abstract

Pick any four one-digit numbers (just so no three digits are the same) and write them down as one four-digit number. Even better, have your fifth- or sixth-grade pupiJs choose the numbers. Now take this number and rearrange the four digits so that they are ordered high to low as you read from left to right. Next, off to the side, again rearrange the digits, this time ordering low to high, and then drop the highest digit so that you have a three-digit number. Now go back and subtract this three-digit number from the high-to-lowordered four-digit number. For example, if you had chosen 3781 your subtraction problem would be 8731 − 137 =?.