You might already know how Christmas is equal to Halloween. You don’t? Well, I came across this some time ago, and it took me a few moments to figure out how Christmas can be equal to Halloween. Now, let me prove to you the truthfulness of that statement.

We have Christmas on 25 December. Let’s put that here:

DEC 25

= 25 [let’s focus on the day, ok?]

= 24 + 1 [it’s obvious I know…]

= (8^1) * 3 + (8^0) * 1 [some fancy arithmetic]

= 31 [of base 8. Much easier to work with than base 3]

= OCT 31 [let’s use the short form of octal]

Wait a minute, OCT 31 looks awfully familiar… Hey it’s Halloween, which falls on 31 October! Thus is Christmas equal to Halloween.

Q.E.D.

Alright, in case you’re not following, the “proof” transformed Christmas and Halloween into their date representations. The date representations happen to be of the form “base-short-form number”. So Christmas became decimal 25, and Halloween became octal 31.

Here’s a lesson to take away. Sometimes, **the problem you’re working on is easier to solve when it’s transformed into another representation**. For example, rotating an image is easier when you transform all the coordinates from raster to Cartesian to polar, and then rotate in polar coordinates. Or change a colour in RGB format into HSL, so you can change colour just by varying the “hue” part.

That’s it for now. Happy holidays!