[E18] Curiously Considering Complex Conundrums (Patreon)

earlier marcello made  a pretty cryptic/alarming post in the devblog...

Today, Ame made a puzzle. She wasn't sure if it was solvable.
Being the maths nerd that I am, she asked if I would help figure out if and how it could be solved.
I couldn't figure it out, so I wrote a program to do it instead.
It took the program 3 minutes and 5 million 'moves' to solve the puzzle.
We decided to put the puzzle in game.
I hope you're all looking forward to E18.

lemme 'splain.

so i'm working on this squest, right, and it has a puzzle. i was kinda looking forward to it, because ever since i decided on it i knew it would be suuuuper easy to implement. like, a little tedious to set up visually, okay... i had kanaya take care of that part for me, and then i was able to do the rest in basically a sitting.

the only thing is, it was easy to make... but easy to solve? mm, not so much.

but critically, it's a numerical puzzle. and i wasn't sure if it was solvable from just any random start. so i decided i'd do it the classic way: build it, and play with it until i figured out if it would work or not. i've done this sometimes. i think i did it with the mirage tower puzzle? i know i did it with  the very end of devonyx's puzzle-- where you go on the spinny things like a bajillion times. i didnt know what that section would look like at first. even now it's not much of a puzzle. but it's pretty fun anyway, ne?

so i pulled in a starting array of numbers from a literal randomizer. what's the odds it's solvable? fuck if i know. is just any solution solvable? fuck if i know. and honestly, i'm not that good at puzzles like this. ^^;
but i know someone who is.
so i bribed dan to test it for me.

after an hour or so, he couldn't get it, so he threw in the towel.
in his defense i caught him right before he was heading to lay down, so maybe he was too tired for it. 

but i was right to ask the lad anyway. i forgot he was good with rubik's cubes. he ended up pulling from his muscle memory of how to work those and transferring it to paper in an attempt to solve this puzzle. honestly, pretty dedicated work for a boy on his way to bed. 

i also used to be decent with the cube. i think my record was just under a minute in high school but fuck if i remember how to do them now xd. but using the patterns he got started, i was able to finish them out and find a solid way to manipulate the puzzle enough so i was pretty sure it was theoretically solvable from my randomized solution, but i couldn't quite pin down the actual solution.

anyway, then marcello got online. 

the thing about marcello is that he is a maths major.
concerning, i know-- but some people like him actually enjoy solutions like these. text logs i guess

Marcello - Today at 2:38 AM
How are you doing?
Amethyst - Today at 2:45 AM
pretty good
i have Created a Connundrum though.
Marcello - Today at 2:46 AM
Curiously Considering Complex Conundrums
What is the ups
Amethyst - Today at 2:48 AM
this is a puzzle that was very easy to make
as it turns out
it is not very easy to solve.
Marcello - Today at 2:50 AM
Let the mathematically illiterate fail and not get their plot😤
Amethyst - Today at 2:51 AM
fortunately for them, this is only a sidequest.
unfortunately dan and i have been trying to solve this for like an hour and a half
😅
Marcello - Today at 2:52 AM
But also yeesh does sound a bit muchskis who would even make  this puzzle am I the questgiver
Also how certain are you its solvable?
Amethyst - Today at 2:53 AM
not very!
that is what i was attempting to find out!
by solving it
Marcello - Today at 2:54 AM
I think if the puzzle's creator can't solve it in 30 mins it should be written off as unsolvable or just too hard
Amethyst - Today at 2:55 AM
i'm fine if it's hard because there are going to be people like yourself that enjoy this, and i'll stack some more rewards behind it anyway
but i just randomized the starting sequence
and have been trying to determine if it can be solved from any position
or not
if it can't
then i can just input the fcorrect solution adn fuck it up and copy that
so it's fine either way
i should probs just do that at this point
Marcello - Today at 2:57 AM
That sounds like a maths problem if you give me the specs of the puzzle I could probably try to work it if it is solvable from any start and, if not, what properties a start needs to be solvable
Amethyst - Today at 2:58 AM
i love it when you talk like that
is that something you would want to do as an exercise/for fun, or would you only do that if i needed that to figure stuff out?
Marcello - Today at 2:59 AM
It sounds fun!
And ahaha, love it when I talk like what ><
Amethyst - Today at 2:59 AM
^~^

so i explained him the puzzle and its rules and he set to work. if he didn't want to do it just for fun, i would've done the working backwards thing i described before. but, you know, why not!

unfortunately he pretty quickly realized...

Marcello - Today at 3:37 AM
The hard part of dping this in general is the sheer number of possible [solutions], given the conditions
Amethyst - Today at 3:37 AM
oops.
Marcello - Today at 3:38 AM
I can't think of a general method by hand for solvability but
Maybe I can write a program
Amethyst - Today at 3:40 AM
this is getting intense.

because just writing quick programs to solve math problems is a thing humans do, i guess????

Marcello - Today at 3:47 AM
And while this is interesting I think I have come up with a cool starting
osition that looks hella jumbled but is in fact like 3 moves from completion for the sake of the actual puzzle, however I'm still working on this program
Oh hey that's awesome my one actually replicates more solutions under row operations that might make it too easy though
Okay yeah I have a jumbled looking square that is very close to completion if you're interested, now to work out an algorithm for this program 😄
Looks moderately jumbled but is 4 moves from done
if players spot the solution ezpz, if not, have fun for an agonizing few hours
--its shell's gym all over again--
Amethyst - Today at 3:59 AM
xd

i was curious so i had him send me the initial set up that he had created, and plugged it into the game to see if i could play around with it and figure out the four move solution. 

i couldn't.

but i was really really close!!!!

meanwhile...

Marcello - Today at 4:03 AM
Oh hey that was fast I wasn't expecting that algorithm to work
I just made an algorithm that randomly made moves and to tell me if it solved it and it did.
So your initial one IS solvable
Amethyst - Today at 4:16 AM
interesting!
Marcello - Today at 4:17 AM
The only thing is I have no real way of counting what moves are and aren't redundant. Lets run it again and have the program tell me what moves it makes, and how many it makes total
Amethyst - Today at 4:18 AM
well, i had just finished the rest of the quest so i was about to go put the one you provided in
but now i wonder 🤔
Marcello - Today at 4:18 AM
Well put in the one I provided and play with it. I'll keep investigating your initial one
Amethyst - Today at 4:18 AM
oki
Marcello - Today at 4:31 AM
Tfw first two times I ran this code it produced a solution, but now I'm running it trying to tell me the number of moves it takes it terminates before working. Which I mean fair, it's totally random, but :////
Amethyst - Today at 4:31 AM
very :/
i'm feeling useless at the one you provided too  😅
Marcello - Today at 4:32 AM
Given the randomness this doesn't help or anything, just provides us with the fact it can be solved
Amethyst - Today at 4:32 AM
as long as it can be solved, it's good with me.
Marcello - Today at 4:33 AM
Given we have 0 clue how to solve the original and there's no guaruntee it doesn't take 10000 moves 👀
Amethyst - Today at 4:35 AM
hhhhhhhhhum.
i cant imagine there's not a more efficient way.
Marcello - Today at 4:38 AM
(Update, random algo did it again and it only took 5546847 moves this time)
Amethyst - Today at 4:38 AM
#learning
Marcello - Today at 4:39 AM
Also interesting yeah that is the solution I started with
I purposefully went for duplicates and non-central stuff not satisfying rules in an attempt to make it harder to spot
(5300168)
(Also of note, it's getting different solutions every time)
(Oh in fact maybe if I grab one of the solutions it spits out it'll be easier for someone to work backwards towards it to see how quickly it can be solved)
Amethyst - Today at 4:41 AM
! tru
Marcello - Today at 4:43 AM
This is the solution my algo just spat out for the initial config, hopefully we can get to it in under 5 million moves
Also how's this for a devblog post :]

Today, Ame made a puzzle. She wasn't sure if it was solvable.
Being the maths geek I am, she asked me if I would help figure out if and how it could be solved.
I couldn't figure it out, so i wrote a program to do it.
It took it 3 minutes and 5 million moves.
We decided to put the puzzle in game.

Amethyst - Today at 4:47 AM
i was definitely planning to make a patron post of it ^^
oml.
ok
do it.
Marcello - Today at 4:48 AM
I am leaving out key parts of information like the inefficiency of the program and the possibility we'll put in an easier variant if we can't figure how to get this soln is reasonable time but y'know
they don't have to know
Amethyst - Today at 4:48 AM
yeeeee
Marcello - Today at 4:49 AM
How's this for the title
A Positively Puzzling Proposition Positing a Plethora of Problems
Amethyst - Today at 4:50 AM
i love it
Marcello - Today at 4:53 AM
Post made :d
Amethyst - Today at 4:53 AM
what a good post

so in the end, we have one solution that we know can be solved in 4 moves.
and one solution that we know can be solved in 5,300,168 moves.
although technically
if you're really dedicated, you could solve the 4 move puzzle in 5,300,168 moves too.

but please don't.

anyway, which set up did we end up going with?
there's only one correct answer there:

both!

so anyway good luck on your story branches or whatever.