https://brilliant.org/wiki/proof-of-divisibility-rules/

The 7 and 13 rules are pretty cool too.

Yep. If the sun of the numbers is divisible by 3, the number is divisible by three.

Works great for 6 too, as if it’s divisible by 3 and even, the number is divisible by 6.

And 9 is the same thing, but the sum has to be divisible by 9 (e.g. 12384 is divisible by 9 because the sum of the digits is 18, which is divisible by 9)

There’s also good rules for 4 and 8 as well. If the last 2 digits are divisible by 4, the whole number is (e.g. 127924 is divisible by 4 because 24 is) and if the last 3 numbers are divisible by 8, the whole number is (e.g. 12709832 is divisible by 8 because 832 is.)

Platypus, my brother in Christ, do you hear how you talk out of both sides of your mouth?

You’d be sad if you had to hang out with people, because you hate that, but you’d be sad if you are alone because you hate that.

It’s not your circumstances making you sad. It’s you. It’s your refusal to engage with your problems because you’d rather languish in your depression.

There’s nothing on earth that could fall into your lap that would make you happy. The world could bend to your will in every way, and you’d still be miserable because the thing making you miserable isn’t external.

You have the power to make 2025 better than 2024. It won’t be easy, and you’ll have to do a lot of things you don’t like doing. That’s life. That’s being an adult. Doing the hard things you don’t want to do to make life better for yourself and the people around you.

And you can do it. But you never will so long as you keep lying to yourself by saying there’s “nothing you can do about it.” There is. You just have to take the first step.