Fun With Numbers

I am a fan of the website Evil Mad Scientist Laboratories. They are not the most frequent to update, but more often than not, those new posts are interesting. I always look forward, however, to their monthly “Linkdumps.” One of these caught my eye this month and I wanted to share it. They linked to a couple of Wikipedia articles about two numbers specifically: 6174 and 1729.

This one is really cool. First, you take any four-digit number that contains at least two different digits (ex. NOT 3333). Next, you make two separate numbers from the digits: one in ascending order, the other in descending (being sure to add buffer zeros if needed). Subtract the smaller number from the larger and repeat with that new number. The cool part is that, in at most seven steps, the number will always converge to 6174. And 6174 continues to repeat itself.

So, an example for you all. We’ll start with the number 7439:
9743 – 3479 = 6264
6642 – 2466 = 4176
7641 – 1467 = 6174!!

The number 495 does the same thing with three-digit numbers.

1729 is interesting because it is the smallest number that can be expressed by adding two positive cubes in two different ways.
1729 = 13 + 123 = 93 + 103
That’s amazing to me considering I’m always taught in my computer science classes about how fast cubes grow.

They also linked to an article about a theory that all numbers are interesting. It’s worth a quick glance, but they prove it by contradiction. If you have a set of numbers said to be “uninteresting,” the fact that there will be a smallest number in that set makes it unique compared to the other numbers and therefore interesting.

And that’s why numbers aren’t trivial, surely among other reasons.


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