too lazy to find a header image

CHAPTER FIVE IS IN A WEEK!?!? A WEEK. ONE WEEK. SEVEN DAYS. A WEEK. A WE

i am so happy about this information

call the ship name "lancer"

Can’t stop thinking about this 236 mile long theoretical PDF. Talked about it on the phone with my friend earlier. PDF longer than the country of Belgium. Forbidden yet technically fully supported 236 mile long PDF. I’m obsessed.

make a PDF of the entirety of Belgium

i just read all the reblogs of this. there were like 50 whole examples. matt rose's audience would love these

Is this true in arbitrary base?

I do not have any sources for that, so i cannot say… sorry!

it can’t be true in arbitrary base because positive integers always start with the same digit in binary, that digit being 1.

I think the original statement needs to be modified somehow to exclude n=0? like, as written I think it is false. anyway this sounds cool! I’m interested in what the proof is like.

I think the right generalization to arbitrary base is something like "if n > 0, then for any b > 2, 2^n, 3^n, ..., and (b-1)^n cannot all have the same leading digit." I'm not sure if this is true in the general case because I think the proof of the base 10 version uses something about 2^n * 5^n = 10^n to only have to worry about 3 being the leading digit (but not sure if that's the right approach I haven't actually worked it out yet)

wait, what? this statement doesn’t make sense for the base 3 case, where it would be saying 2^n cannot have the same leading digit as itself for all n > 0. you also have a counterexample very quickly in base 4, as 2^4 and 3^4 give you 100_4 and 1101_4, respectively.

it's only true in bases that aren't prime powers

There should be two of these. They're part of a magic trick where you split a 7 of diamonds into two 3½s

if anyone would be so kind as to scroll through this person's entire blog and count all the poll distributions

you have travelled too far back in time. please scroll back up to return the earth to its normal state

This reminds me of a joke I have with two of my cousins

this reminds me of two jokes i have with three of your cousins

This reminds me of the three jokes I have with four of our cousins

This reminds me of the joke i have with both of your moms

i wish i had that many oreos

I enjoy when video game mechanics fuck up in ways that provide insight into the particulars of their implementation. Like, my aerial controls just went screwy because somewhere below me there was a section of icy floor? Fascinating – let's see what other deranged implementation details I can puzzle out.

bugs are my favorite rule discovery puzzle game

i don’t need to say it

don’t say anything. just reblog this if you’re thinking of exactly that thing when you see this picture