When playing around with a few ideas for a numeral system for a fictional culture in a game idea I kinda work on in the back of my mind, I came up with this system:

If you figure out how the first two add up, hopefully that should be enough info to solve A3 and A4.

If you solved the above, this one below (using the same visuals, but with different meanings) is harder:

They aren't really "puzzles", more like deciphering the symbols to understand how the system works.

If you solve it, post the answer in spoiler tags:

[spoiler][/spoiler]

I think I've got A, working out B now.

[spoiler]Each row is 5^(n-1) where n is the row index. So it goes 1 5 25 125 625. Add each column together. Which makes A3 = 780 and A4 = 3124.[/spoiler]

edit: fixed mistype in A3 answer.

slicer4ever solved A, so here's B.

[spoiler]

B: Each ring is a five digit number in binary, with each of the five bars in the ring being one digit: the ones place at the 12 o'clock position, counting up clockwise (1s, 2s, 4s, 8s, 16s). The entire symbol is a five digit number in base 32, with each of the five rings being one digit: the ones place in the center, counting up outwards (1s, 32s, 1024s, 32768s, 1048576s).

B1: (1 + 2 + 8)*1 + (2 + 4 + 16)*32 + (1 + 2 + 4 + 8)*1024 = 16075

B2: (4 + 8 + 16)*1 + (1 + 2 + 4 + 8 + 16)*32 + (4 + 8)*1024 + (1)*32768 = 47076

B3: (1 + 2 + 4 + 8 + 16)*1 + (1 + 2 + 4 + 8 + 16)*32 + (1 + 2 + 4 + 8 + 16)*1024 + (1 + 2 + 4 + 8 + 16)*32768 = 1048575

B4: (2 + 4 + 8 + 16)*1 + (2 + 4 + 8 + 16)*32 + (2 + 4 + 8 + 16)*1024 + (2 + 4 + 8 + 16)*32768 + (2 + 4 + 8 + 16)*1048576 = 32472030

[/spoiler]

edit: fixed mistype in B4 answer. (Yes, both of us apparently.)

man, i was looking at B entirely wrong. I kept trying to figure out a solution for B that was in a similar line to A. don't think i'd ever have come up with the answer. very nicely done Equality. I'm curious how SotL came up with these puzzles.

I guess the solution was the culmination of three lines of thought:

[spoiler]

"base five is a red-herring"; "maybe I'm supposed to read this symbol in a non-obvious direction"; and "base two makes a lot of sense here".

Lots of trail and error was involved in getting there. At one point, I was even trying to read the thing in a spiral pattern.

[/spoiler]

Fantastic, gentlemen!

[spoiler]The answer to B4 is 32472030; you multiplied the last value by 1048567 when it should be 1048576 (the last two digits were swapped, I think).

Your solution is fully correct! Binary digit from 12-oclock around, and from the inner ring out.

Though, you can just unfurl all the rings into a single line of binary digits - no need to view each ring as separated.[/spoiler]

I PM'd you both a copy of the current Frozenbyte humble bundle. I hope you enjoy it!

I've been a long-time fan of their games, and greatly enjoy both the Trine and Shadowgrounds series (both series are best played cooperatively on a single PC, and would require a controller for local coop - though singleplayer and online coop are also playable).

I'm curious how SotL came up with these puzzles.

I'm really heavy into background lore and world design, so I get alot of little snippets of ideas for lore and town layouts and languages. One thing I've been (very casually) playing with is fictional languages and the structures of grammars and root words of languages (mostly Greek, Hebrew, and Latin - again, very casually - I don't actually know any of those languages). So two days ago, chatting with a relative, they pointed out that our numeral system is based upon line segments (at least for the first four digits):

[spoiler]

[/spoiler]

So then I created this as a fictional numeral system:

[spoiler](The below is entirely fictional)

The above is entirely fictional - we'd never be so meaningless in real life as to divide a circle into some arbitrary number of segments like 360 'degrees'. What nonsense! [/spoiler]

Pardon my poorly written English in those images. Sentence Fragment (consider revising)

When jotting down design notes, I drop out some 'unnecessary' words so I can write faster before I start forgetting the ideas.

that's very cool SotL. imo, it'd be pretty fun to place these into a game, not as a primary puzzle, but perhaps some sort or secondary story puzzle that can be resolved into words, i could imagine finding these drawings etched into the side of walls, to most players it's meaningless, but to the dedicated players that solve the puzzle, it could give a deeper satisfaction to the story.

What irks me about A is that there is no single symbol for a number, but a bunch.