I don't know how well this puzzle will translate to a toot. Imagine each line is on a card:

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

Put them in order.
(The 5th graders could do it, but they did have a helpful example first... There may be more than one solution, but I think there is ONE really good order. Can you find it?)

(I should also mention that every adult I've shown this to gives up. But I only showed it to two rather grouchy teachers.)

Yeah this is harder without cards to move around and put in arrays. But I think it's still possible.

@futurebird order of what?
Make a related, transform sequence starting the first “card”?

@dahukanna

Imagine you have been learning to count in base 2, 3, 4 just before being asked to do this.

However, if the order can be explained with a few simple rules it's valid IMO.

@futurebird

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

Possible Solution.

@golgaloth

is this alphabetized?

@futurebird
This is a question that makes me unreasonably annoyed if not angry. Without having seen an existing order there's huge amount of possible and equally valid sollutions.

Easy one is to arbitarily assign each symbol a number and read the card as base ten, e.g. first one could be 112 or 443. Then there's the question of how each value is ordered. Ascending, descending or by maybe divide them into subgroups by some arcane mathematical rule and order those someway.

Just... Reminds me of school in the Not Good way

@MxSpoon

Ok what if I tell you

▷ is first

WRONG: □▷▷ is last

RIGHT: □□▣ is last

I think that narrows down the valid solutions a lot.

I apologize. I gave an unhelpful hint here. It's late.

(I glanced over at the incorrect list.)

@futurebird is it base 4?

@futurebird other than 0 which never starts a multi-digit number i don’t see how can one assign other digits to symbols

@xarvos

There is more than one valid solution.

@futurebird I like this. When I teach people about bases, I try to break them free from the symbols having values, and we often end up having them do something in base 3 with circles, squares, and triangles.

@mason

Funny you should mention that.

@futurebird i tried copypasting into a plaintext editor but some of the line-initial "▣"s got garbled into tofu -_-

@apophis

What symbols do you like I can do find replace?

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

@apophis

I gave you some ASCII for extra safety.

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

@apophis

This looks scary:

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

@apophis

Well I feel that there is a logic to:

▷
□
■
▣

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

@futurebird oh wow this feels way easier

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

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

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

*
[
-
^

[*
[[
[-
[^

-*
-[
--
-^

^*
^[
^-
^^

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

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

Here is the real puzzle. l

@futurebird I am confident the beetle will solve it

@VoiceofDuum

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

@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.

@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

@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

@bri7 @c9a

Ah! grey. That makes more sense.