After a period of thought, you approach the door triumphantly in order to type in
as the keycode.
As you do so, you recall the reasoning that led you to this conclusion. Putting together the torn sticker, you saw a number of strange symbols in a gridlike shape. Fortunately for you, a calling card was left on the scene, describing the working mechanism of the locking machine. This struck you as a rather odd security practice, but you were not going to look a gift horse in the mouth.
This indicates that some rays should be traced from some starting points, turning, splitting and stopping according to some rules. You wondered what these rules could be, and reached the conclusion that the strange symbols were surely involved.
The grid had a number of those symbols, but after analyzing all of the available information, the meaning of each slowly became clear.
The easiest one to determine was #, thanks to the help of a previous unworthy puzzler who left his note on the floor. He might have failed in his mission, but you were sure you wouldn't do the same.
The image indicates that a ray incident to the # symbol splits into 3 different rays, one in each direction.
Following that, you remembered another odd piece of paper you had found. > and < didn't take long to fall.
After tracing the paths between the numbers listed, you realize that the paths are perfectly described on the right if the symbols > and < indicate right and left turns, respectively.
The writing on the wall seemed out of place. You thought maybe the placement of the @ symbol was important.
If nothing goes through the @, then you reason it should be a ray blocker of some sort.
The lowercase letters seemed impossible to crack. As a desperate attempt, you look through the peephole, when suddenly it opens to reveal someone looking back at you. Despite nearly dying of a heart attack, you manage to recall some very important schematics inside the room...
You notice that the colors in the drawing are blue, cyan, green, magenta, red and yellow, which have a 1-to-1 correspondence with the lowercase letters in the grid: bcgmry. The bottom picture, coupled with the fact that there are two of each of those letters in the grid, suggested those letters should act as portals, teleporting rays from one point of the grid to the other.
But you were clueless as to how any of this would precisely help you. Even if you figured out the inner workings of the system, how would that possibly help with getting in the door? You go back to the note on the ground...
You thought this could mean there is an input-output relationship between the entered code and what the display shows. Thanks to your fiddling with the terminal earlier, you already knew another input-output pair right off the bat: 0001 = DONTGUESS. You recall an interesting line you saw earlier...
It would make a lot of sense if the display produced the word "ENIGMATIC" when the right sequence was pressed. You now noticed that all the letters necessary to spell ENTERPASSCODE, DONTGUESS and ENIGMATIC were present in the grid, so the words were likely being formed by some interaction between the rays and these letters.
The numbers were still unaccounted for. But with your previous guesses, it only made sense that...
the numbers you typed into the machine were being used as starting points for the raycasting. But there were 4 spaces for numbers, so how could this relate to the points? Would that be related to this part of the note on the ground?
You remember the ramblings of your friend @f'' about combinatorics, and how those numbers represented the number of ways to pick 4 digits with order, 4 distinct digits with order, 4 digits without order and 4 distinct digits without order. You never thought any of that would ever be useful, yet here you are. This clued you to the fact that the order of the digits in the password does not matter: pressing the 0 button causes rays to be shot from all zeros in the grid.
All pieces had nearly fallen into place. But you heard beforehand that most puzzlers that dared to open this door were thwarted by a single symbol. Surely enough, you only had a single symbol left: %, and it was proving to be quite the tricky beast. Maybe...
The previous puzzler's notes suggest % is a line shy from being an X, which indicates blocking of some sort. In its initial state, % is open, but whenever one ray passes through this square, it becomes a blocker for further rays. In conclusion, if two or more rays hit this square, they are stopped on their tracks, but a single ray should be able to make it out.
At this point, all of it was purely conjecture. But remembering you had two output pairs, did they confirm your theories? You had to test it to find out.
What happens when rays from all zeros are cast?
You read the uppercase letters crossed by the rays from top to bottom, left to right: "ENTERPASSCODE". You must be on to something! The next step is to try it out with 0001:
You noticed the pink square is a paradox, because letting a ray through it would allow it to loop around to the pink square, blocking itself. You then assumed whoever engineered the system dealt with this somehow, possibly by blocking the ray outright. Making that assumption, the uppercase letters form "DONTGUESS"! Couldn't be a coincidence, could it?
All that was left was figuring out the combination to open the door. By using some process of elimination to quickly weed out numbers that couldn't be present in the final passcode, you reached your most likely candidate.
Most of the numbers caused the rays to immediately pass through letters not in ENIGMATIC. In fact, the only 4 numbers you saw that did not were 2,3,6 and 9. What happens when you use these 4 as starting points?
You read the crossed letters: ENIGMATIC!
Were you finally worthy? There's only one way to find out. You reach for the keypad...