Eternal Algebra Class Withfour

Eternal Algebra Class Withfour (or its official acronym, EXIT, even though the acronym spells out Eternal Xalgebra Iclass Twithfour), or simply Eternal Algebra Class (mentioned by Balloony), is where contestants go after they are eliminated in Battle for BFDI.

In EXIT, characters seemingly have to endure endless lessons and worksheets about algebra.

Four also shows suspicion about how Balloony knows about EXIT, and it is also unknown why Eternal Algebra Class's existence shouldn't be known, more or less as a secret.

It was not until Enter the Exit that Eternal Algebra Class was finally seen onscreen.

Appearance
Eternal Algebra Class consists of two parts within Four. The outside of the room is a dark and endless plane. A door connects the abyss with the classroom.

The classroom consists of pale blue painted walls, a chalkboard, a teacher desk, and numerous student desks. Lining the walls are multitudes of corkboards and posters. Oddly, the environment is completely rendered in three dimensions, whilst the characters remain two-dimensional. Elongated fluorescent lights brighten the room, attached to the ceiling. The wall adjacent to the door holds two long windows, yet only pure white can be seen "outside".

On the chalkboard, there is:
 * A message saying "Do the worksheet... or else"
 * The quadratic formula, which equals a drawing of X
 * A drawing of Ice Cube with hearts nearby, probably drawn by Bracelety
 * An equation saying that one cat plus one cat equals 2

On the teacher's desk, there is a to-do list presumably written by Four. The contents written on it are as follows: The last task written likely alludes to how Four quickly screeched at Clock in an earlier scene.
 * thank Pin
 * get David
 * get 8-Ball
 * get Stapy
 * get Loser
 * get Roboty
 * do rejoins
 * KILL CLOCK

In the back of the room, there are two cork boards. The one on the left has two papers each with computers drawn on them, as well as some small writing that cannot be read. Perhaps, it is rules for the computer in that same area of the room. The other paper on the left cork board is a chart with Bracelety's name on it as well as some intervals of time written on it. This is a chart of Bracelety, Liy, and Leafy's computer time.

The cork board on the right is labelled "My Project", and has four papers, each with one contestant's name on it. These are likely projects that each of the eliminated contestants made. There is writing on all of the projects but is too small to read. The images, however, allude to what the projects are about. Liy's project features an image of a coordinate plane with a smiley face on it, Bracelety's project has the function y4 = 1 - x4written on it (which, when graphed, resembles a picture of Ice Cube), and Pencil's project has the equation A = √3 a2 written on it. Leafy's project, however, is rather mysterious. It has lots of pairs of numbers written on it, written large and clearly.

They look like coordinates because of the way the pairs are written, but when plotted on a coordinate plane, it results in this (shown right), which resembles the path that Leafy took with avoiding the nails in "Lofty" and the acid spitballs in "Get Digging". It also resembles the same path that Spongy took avoiding the lasers in Gardening Hero.

A more likely answer is that these are the "subtraction by 1" exercises that Pencil had mentioned, as well as some similar exercises. However, none of the equations appear to be solved, and there is also no other writing on her project.

In one of the corners of the class, a photo copier/printer is found, with the text "Ready" on its screen. On a nearby wall, there are four pages with the text "SEE YOU SOON ICE CUBE". Near it, a page is pinned to the wall with the text "÷ 5÷6=0.83333333". There's also an old TV used to play the Cake at Stake theme when the contestants were rejoining.

The room is updated with Roboty, Loser, 8-Ball, Stapy and David's projects in episode 11, Get to the Top in 500 Steps. Roboty's consists solely of Morse code with no graph or equation shown, Loser's is completely blank aside from his name, and 8-Ball's contains unreadable writing and the equation ᵃ√(16777215+1), where 16777215+1 = 8^8. Stapy's seems to depict a large irregular shape with a black arrow emitting off of a nearby smaller shape, and David's contains only a single, unreadable word.

Class activity
Of course, with the name of Eternal Algebra Class, and the appearance of a classroom, the eliminated contestants spend time doing algebra related activities. Pencil states that they perform activities such as "subtracting by 1" exercises, quizzes about graphing the y-axis, and rituals of the holiness of one digit even number perfect squares (the only one of which is 4, if you ignore negative numbers, numbers in different bases and 0). In Enter the Exit, the contestants are shown doing a quiz or test (a replica shown on the right). There are six questions, as well as a bonus question. Each question results in the answer of 4, ironically excluding the 4th question, which results in the answer of -4.

Each contestant's quiz is done in a different way depending on each character. Pencil appears very disinterested, with doodles all over her quiz, Bracelety enters "ICE CUBE" in large letters to answer every question except the bonus question (which is 4), and Liy is taking a straight forward approach, simply answering the questions. She is shown apparently stuck on Question 4. She had also written the phrase "How can I show my work for this?" on question 1, seeing as how it's a very basic subtraction problem.

The questions 4 and 5 are 4/4+4/4+4/4+4/4 and factoring n^2+8n+16, which factors into (n+4)^2.

In episode 11, Get to the Top in 500 Steps, it is revealed what the rest of the contestants had done for their quizzes. Neither Loser nor Roboty wrote anything on their quizzes. 8-Ball had answered questions 1 and 2 correctly but had done 3 through 6 wrong, answering them all with 8. He also wrote the phrase "I don't have one" on the bonus question, referencing his denial for having a favorite number. David had simply written the word "NO!" on the paper in gigantic, scribbled text. Stapy had only written the number 4 on each question, except for the bonus question, with no work shown. Finally, Leafy had answered questions 1 and 2, as well as the bonus question, where she writes about how hard it is for her to tell. Questions 3 through 6 are not answered, and there are scribbles and doodles much simpler than the ones on Pencil's quiz.

Contestants currently eliminated/in EXIT
The contestants are listed in the order they are voted off.

Seating chart
The Exitors appear to be seated based in the order that they were eliminated. It is unknown where contestants eliminated after Get to the Top in 500 Steps are seated, as EXIT has not appeared since then.

Trivia

 * Four refers to EXIT using multiple terms and euphemisms, such as "sleeping" or "getting poo-pooed".
 * Leafy is currently the only contestant to leave EXIT, re-joining the Battle For BFDI in Get to the Top in 500 Steps, with 13835 voters thinking she should rejoin the Battle for BFDI, not being in team Beep, but going to The Losers! instead.
 * Before she rejoined, her seat was between Bracelety and Pencil.
 * Pencil references Four by saying "appreciation rituals of the holiness of single-digit even perfect squares".
 * The only single-digit perfect even squares are 0 and 4, so she may or may not be referencing Donut (zero) as well.
 * Coincidentally, Donut became a host after being multiplied by four.
 * The cat drawing on the chalkboard referenced an April fools video that Jacknjellify made, called "Add 'em cats; there are two!"
 * Contestants in EXIT are referred to as "Exitors".
 * On Pencil's desk, a drawing of all the female Exitors are present.
 * Additionally, a drawing of Pencil's alliance next to the Yoyle Needy is also present on her desk.
 * Furthermore, there is also a drawing of Four in the form of a "Cool S" on her desk.
 * One of the chairs has light blue text that reads "Grupheetie" written on it.
 * This might be a reference to the Recovery Centers.
 * When Pencil's chair nearly falls over, her reaction is the same pose she has in the intro of Battle for BFDI.
 * During rejoining auditions, Pencil's chant is a reference to to her "Vote for me, yeah yeah yeah!" chant from previous seasons.
 * The chant goes "Vote for me, yeah yeah yeah! Type an [A], yeah yeah yeah! 'Cause my alliance NEEDS me! They just can't live without me!!"
 * While Four was dead (or factorized), EXIT continued to exist, as the contestants inside had to do a certain worksheet numerous times.
 * The objects in EXIT are seated in a specific order, based on the time of their elimination.
 * The first three objects eliminated sit in the right column (from the teacher's point of view, from back row to front row. The fourth to sixth eliminated contestants sit in the middle row, etc.
 * The question "64-1", mentioned by Pencil, may be a reference to her elimination, where the number of contestants still in went from 64 to 63.
 * If one looks closely at the cameras, Four and the eliminated contestants can't be seen.
 * The EXIT is made in CGI.