I came across a math puzzle here in the fediverse, and puzzled about it for a while. (Lost the link to the original post; if it’s yours let me know.)

Here’s the problem:

Bob was given 30 distinct natural numbers. He wrote down all the 435 pairwise sums.  It appears that among those sums, 230 are divisible by 3.  How many of the original 30 numbers are divisible by 3?

I was able to find the answer after playing with it for a bit. Then I made this cool visualization. (It’s a spoiler, of course.)