Why Happy Numbers are Also the Naughtiest Numbers in History

Illustration for article titled Why Happy Numbers are Also the Naughtiest Numbers in History

A while back we had a post about how Happy Numbers and the Spiral of Four make up a sort of binary code for all numbers in existence. We thought that was all there was to say. How wrong we were! A reader wrote in, giving me more information on how his math class made Happy Numbers the naughtiest numbers in history.


I recently posted about Happy Numbers. They're a mathematical concept with no known origin. They were first documented in the 20th century, when the child of a mathematics professor told her father that she had learned about them at school, but he was unable to trace the idea back to any point of origin. It seems they came out of nowhere.

Finding Happy Numbers isn't nearly as hard as finding their origin. Take a number - say 31 - and separate out the digits. Square each of the digits and add the squares together. You'll have a new number to repeat the cycle with. Thirty-one is 9 plus 1, which equals 10. The same process with 10 reduces down to one. Any number that, eventually, reduces down to one is a Happy Number. Any number that doesn't will get trapped into a never-ending cycle of digits, the smallest of which is four. It will loop around to four again and again, never reducing further.

While no one has claimed to be the originator of Happy Numbers, plenty of people have staked other claims. Once the concept came out, it was a veritable gold rush to find different types of Happy Numbers. There were Happy Primes, and the largest Happy Number with no repeating digit, and the largest and smallest pandigital Happy Numbers.

But one reader, who was in a math class that advanced the field of Happy Numbers, wrote in to let me know that mathematicians were not above doing more than making numbers "happy." As his class did research on different concepts in Happy Numbers, they went wild with the names. The tamest name they gave out was to 31 and 32. They pronounced them a "loveable couple," since they were the first adjacent pair of Happy Numbers. Things weren't quite so innocent from there on in. They officially termed any three Happy Numbers in a row a Menage a Trois. But they hit pop-culture paydirt when they found the first set of four Happy Numbers in a row. The numbers 11248, 11249, 11250, and 11251 were called Bob, Carol, Ted and Alice, after the title of a recent movie about two couples and their attempt to be swingers.

Of course, the class did eventually get their minds out of the gutter and theorized about ever-greater consecutive Happy Numbers without giving them naughty names, but I think it's a testament to both research and the persistent insouciance of the student mind that there are sexy terms even for concepts in pure math. Let that be an inspiration to all theorists. Find more Happy.




That professor didn't just go and ask his child's teacher where they got it from?

"Hmmm, this great mystery. I wonder where it could have come from? It's really too bad that there is no way to get more information. I guess the world will never know."