I've had this puzzle on my phone for years. Every few months I'd glance at it and try and solve it. Last night, as I was eating dinner, I finally figured out the answer!

https://sh.itjust.works/post/55641581

Hah, took me nearly a minute.

Tap for spoiler

Add the digits on both sides. ? = 12

But I only got it so quickly because I enjoyed a similar puzzle once.

1
11
21
1211
111221
312211

continue the series.

312211

13112221
1113213211
31131211131221

Wonder if/when a 4 would ever show up… and what the formula for that would look like

Think about it.

To get a 4, you need either 1111, which can’t happen because thats just 21, or you have 211112, which would again just be 31.

Seems you can’t have a series that ends in anything but 1, if it starts from 1?

2
12
1112
3112
132112
1113122112
311311222112
13211321322112
1113122113121113222112

I wonder if this type of series would eventually become repeating… or is it irrational?

Still curious what the mathematical proof would look like. Not that I’d be able to understand it regardless, but curious nonetheless