I don't know how well this puzzle will translate to a toot.

[futurebird@sauropods.win]

@apophis

What symbols do you like I can do find replace?

[clayfoot@mastodon.social]

@futurebird

4 symbols, so maybe base-4 number system
24 "cards" so assume 0-23
Only 1 base-4 number in that range has 3 of the same digit: 111 (21). So □ must be 1.
Only 9 3-digit numbers in that range, and only 1 of them is 1 followed by 2 digits: 100 (16). So ▷ must be 0.
Digits 2 & 3 will have to wait until I get home.

[futurebird@sauropods.win]

@apophis

This looks scary:

[[*
[[[
--
-
[-
[*^
^
[^
-*
-^
^*
[[-
[*
^^
[[
[
^[
[[^
-[
*
[*[
[*-
^-
[**

[apophis@kill-corporations.enterprises]

@futurebird the more common unicode emojis might be safer...

[futurebird@sauropods.win]

@apophis

I gave you some ASCII for extra safety.

[apophis@kill-corporations.enterprises]

@futurebird (now i'm wondering if anyone's going to decide on their best "one true" answer by going in unicode order)

[futurebird@sauropods.win]

@apophis

Well I feel that there is a logic to:

▷
□
■
▣

But, beyond the triangle I think you can reorder the other three.

[apophis@kill-corporations.enterprises]

@futurebird oh wow this feels way easier

sorting into 3 groups by length, then sorting by first glyph in each...

[limnobotanik@norden.social]

@futurebird @apophis ah i would have reversed the two last ones. But that wouldn't make a difference, would it?

[bkim@mastodon.social]

@golgaloth @futurebird I hate it when the file stage1.txt is followed by stage10.txt instead of stage2.txt, but it happens

[apophis@kill-corporations.enterprises]

originally had "[" as 3 because i was thinking sloppily and figured "big string = big number" but the error was obvious once i'd sorted the [-initial 3-longs into their sequenced groups of 4 at the end and it was clearly skipping a few series

the -^ order was entirely arbitrary

*
[
-
^

[*
[[
[-
[^

-*
-[
--
-^

^*
^[
^-
^^

[**
[*[
[*-
[*^

[[*
[[[
[[-
[[^

[gaditb@icosahedron.website]

@futurebird You're connecting it to your digits definitely gave me a lot, I don't know if I'd have had a first thought without it.

▷ : only ever occurs on the right side in "▷", has something to its left otherwise. So numbers go right-to-left and "▷" is 0.

□ : is the only thing that's on the right of a three-symbol sequence. So since there's only one symbol in that position, it's a 1.

That said, I think there are TWO equivent orders. You could have either removed 1 card, or added up to 7 cards, or added 9 to... maybe 38, I think, and made it unambiguous, but what was given was ambiguous:

▷
□

▣
■

□▷
□□

□▣
□■

▣▷
▣□

▣▣
▣■

■▷
■□

■▣
■■

□▷▷
□▷□

□▷▣
□▷■

□□▷
□□□

□□▣
□□■

--

The remaining symbols are "▣" and "■", and they occur entirely symmetrically. So we can use the shapes themselves to judge --

either it goes ▷, □, ▣, ■ -- filling more of the square each time,

or else it goes ▷, □, ■, ▣ -- where □+■=▣ because ▣ is "a filled square ■ in an outline □".

[gaditb@icosahedron.website]

@futurebird ... also tho, are the cards oriented.

Because if □□▣ can alternatively be ▣□□, I haven't tried it out but I'm pretty sure that changes things.

[golgaloth@writing.exchange]

@futurebird You said order. I'm a writer.

[futurebird@sauropods.win]

@gaditb

Two cards that could be flipped where the last two the students fit into their pattern.

They decided that having a repeat made no sense.

[heliograph@mastodon.au]

@golgaloth you win the writers' internet today @futurebird

[sjb@mstdn.io]

@futurebird
□
□□
□□□
□□■
□□▣
□□▷
□■
□▣
□▷
□▷□
□▷■
□▷▣
□▷▷
■
■□
■■
■▣
■▷
▣
▣□
▣■
▣▣
▣▷
▷

[mason@partychickens.net]

@futurebird

I don't see a way to determine if ■ is two or three, and ▣ is whichever of those that ■ is not. ▷ is zero. □ is one. Thus, depending on how you assign the two filled-in squares, the order is either

▷
□
■
▣
□ ▷
□ □
□ ■
□ ▣
■ ▷
■ □
■ ■
■ ▣
▣ ▷
▣ □
▣ ■
▣ ▣
□ ▷ ▷
□ ▷ □
□ ▷ ■
□ ▷ ▣
□ □ ▷
□ □ □
□ □ ■
□ □ ▣

or

▷
□
▣
■
□ ▷
□ □
□ ▣
□ ■
▣ ▷
▣ □
▣ ▣
▣ ■
■ ▷
■ □
■ ▣
■ ■
□ ▷ ▷
□ ▷ □
□ ▷ ▣
□ ▷ ■
□ □ ▷
□ □ □
□ □ ▣
□ □ ■

I suspect the ordering of ■ and ▣ is arbitrary given that □ is definitely 1, which makes them all somewhat out of order if we consider the unicode values.

▷ 25b7
□ 25a1
■ 25a0
▣ 25a3

I like patterns. Thank you again.

[stveje@mstdn.social]

@futurebird ▷ 001
□ 002
▣ 003
■ 004
□▷ 021
□□ 022
□▣ 023
□■ 024
▣▷ 031
▣□ 032
▣▣ 033
▣■ 034
■▷ 041
■□ 042
■▣ 043
■■ 044
□▷▷ 211
□▷□ 212
□▷▣ 213
□▷■ 214
□□▷ 221
□□□ 222
□□▣ 223
□□■ 224

[ingalovinde@embracing.space]

@futurebird I'm an adult, and this looks like numbers to me. There are only four letters and too many combinations made of these letters, so it's unlikely that they are words rather than numbers in base-4. (Words written with alphabet typically have much more redundant encoding with much fewer allowed combinations)
There are four single-character numbers and 12 two-character, with all possible combinations of the characters except the leading triangle in two-character numbers, no language behaves like that.
None of the numbers (besides single-character triangle) start with triangle, so I'd guess that's 0 and they're written in the same direction as our Arabic numerals. And another guess is that the list is a contiguous chunk of numbers (because at least it contains all numbers from 0 to 15)
All three-digit numbers start with empty square, so I'd guess that's 1.
All three-digit numbers start with either 10 or 11, further confirming the "contiguous range" hypothesis. There are all four possible combinations starting with 10, but only three starting with 11, so they must be 110, 111 (we already know how these look like) and 112. Therefore, nested squares is 2.

Final answer:
* It's a base-4 alphabet, encoding all integers from 0 to 112 (22 in decimal)
* Triangle is 0
* Empty square is 1
* Empty square with nested filled square is 2
* Filled square is 3