Mysterious 6174

I want to let you in on one of our favourite mathematical mysteries... To get started, choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

We'll show you what we mean with the number 2005. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

5200 - 0025 = 5175
7551 - 1557 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174

When we reach 6174 the process repeats itself, returning 6174 every time.


Now try with your four digit number... what do you get? I bet you'll get to 6174, every time, no matter what number you chose! Try a few more and see if you believe me!

Do you think we always reach the mysterious number 6174? If we do, why do you think that happens? If this mystery piques your interest, then you can find out why in this excellent article by Yutaka Nishiyama. This question has been intriguing Plus readers for years, and Yutaka's article remains one of our most popular articles, generating reams of comments, emails and discussions. And spoiler alert - 6174 isn't the only number with these special numbers - but you'll have to try the same process with three digit numbers, or read the article, to find out!