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

[clayfoot@mastodon.social]

@futurebird

I think assignment of ▣ and ■ is arbitrary, so I'm going to choose 2 and 3 just to make it easier to remember:
0 -> empty -> □
1 -> partial -> ▣
2 -> filled -> ■
3 -> triangle -> ▷
I can then sort the cards easily
0 to 23 in base 10, or
0 to 113 in base 4, or
□ to ▣▣▷ with the cards

[futurebird@sauropods.win]

Here is the real puzzle. l

[gemini6ice@hachyderm.io]

@futurebird linear ordering?

[ronjeffries@mastodon.social]

@futurebird two of these things are not like the others

[braxa26@mindly.social]

@futurebird The puzzle would probably take me hours to solve; I'll just admire the giant stag beetle (I think?) for a while. 😁

[anselmschueler@ieji.de]

@futurebird Assuming you're using ▷ to represent the red triangle, it seems to me like there's a card that appears twice in the image but not in your list. Namely the one at the top and at the bottom right, which I'd render as ▷■. At the top the triangle is rotated differently so it's perhaps ■▷? Still, I can't find both of those in the textual representation

[anselmschueler@ieji.de]

@futurebird I haven't checked exhaustively, but it seems to me that interpreting this as base 4 is sensible, and you can deduce that ▷=0 and □=1, but I don't see a way to pin down the values of ▣■…

[voiceofduum@mindly.social]

@futurebird I am confident the beetle will solve it

[jgrg@mstdn.science]

@futurebird

1 □
2 ■
3 ▣
4 ▷
11 □□
12 □■
13 □▣
14 □▷
21 ■□
22 ■■
23 ■▣
24 ■▷
31 ▣□
32 ▣■
33 ▣▣
34 ▣▷
111 □□□
112 □□■
113 □□▣
114 □□▷
141 □▷□
142 □▷■
143 □▷▣
144 □▷▷

[jgrg@mstdn.science]

@futurebird Digits fixed, now that I've identified the zero, and it is base 4:

0 ▷
1 □
2 ▣
3 ■
10 □▷
11 □□
12 □▣
13 □■
20 ▣▷
21 ▣□
22 ▣▣
23 ▣■
30 ■▷
31 ■□
32 ■▣
33 ■■
100 □▷▷
101 □▷□
102 □▷▣
103 □▷■
110 □□▷
111 □□□
112 □□▣
113 □□■

[futurebird@sauropods.win]

@VoiceofDuum

He's very frustrated that it takes so long to move each card to a new location.

[jgrg@mstdn.science]

@futurebird If you were to remove the zero card and add a 120 card, then the order would be unambiguous. The symbols for 2 and 3 are currently interchangeable, leaving two solutions.

[ingalovinde@embracing.space]

@futurebird once again we have four characters, four cards with each of the characters, and 12 cards with two-character combinations, so I'm just going to assume it's like the last time, base-4.
On 12 two-character cards, we get one with two triangles, one with two filled circles, one with two squares, but none with two empty circles. Therefore empty circle is zero.
Now from the card with empty circle and triangle we can deduce that if we write digits in the same order as usual, more senior to the left, less senior to the right, then the correct orientation of triangle is the one where the right angle is to the bottom left of diagonal.
Rotating all cards with triangles to their right orientation, we see that in three-digit numbers, triangles only occur in the rightmost position, and in the leftmost it's always filled circle. This probably means that filled circle means 1.
"Filled circle, square, empty circle" card is oriented properly because empty circle is zero. But we never see a three-digit number with triangle in the middle. Assuming, like in the previous puzzle, that the numbers are consequential, we get that square is 2 and triangle is 3.

The numbers on the cards are, in base-4 with Arabic digits:
32 in the second (only) column of the top row.
31, 20, 11, 2.
113, 103, 100, 13.
0, 3, 102, 12 or 21 (impossible to determine if it's upside down or not).
120, 101, 30, 22.
112, 110, 33, 1.
111, 21 or 12, 23, 10.

[lufthans@mastodon.social]

@futurebird @xarvos There are 24 lines in your box empty, box full, box outline, triangle example. I swapped to , " : > to work in terminal

It seems one more or one fewer would allow determining which is the 3rd and which is 4th symbol

Your card example has 25 cards, and a beetle assistant, so I skipped to 3 symbol cards and I believe the 25th card solidifies the order as:

circle
earth
square
triangle

For the cards also had to figure out left to right order, but I think I got that correct

[lufthans@mastodon.social]

@futurebird @buddhawilliams woohoo! Got it right

Granted, if I understand it correctly, that was a 50/50 on correct or incorrect :)

[futurebird@sauropods.win]

@c9a

1. I'm confused by your ordering. It's not alphabettized, and it's not a base 4 analog. That doesn't mean it's not logical, hmmm.

2. I'm impressed by the little application. What language did you use? My CS club students are making some web games and they want to do things like save scores and let users compare answers so this could work.
As such JavaScript isn't sufficent. Too client side. We've been trying PHP.

I used to be a web dev but that was two decades ago.

[mensrea@freeradical.zone]

@futurebird without other context we can assume that it is potentially in the correct order already, as these could be words rather than just random groups of symbols

[bri7@social.treehouse.systems]

@futurebird @c9a looking at the criteria, it’s a valid grey code, making it transformable to a base 4 ordering by reflection rules, and also transformable to a valid towers of hanoi solution

in theory. i haven’t validated any of these claims

[bri7@social.treehouse.systems]

@futurebird @c9a if valid, by “reflection rules” i mean that splitting it in half, and reversing one of the halves… then repeating on each half recursively, should result in a base4

[futurebird@sauropods.win]

@bri7 @c9a

Ah! grey. That makes more sense.