Eternal Algebra Class Withfour

""Sleeping" is Four's codeword for elimination and Eternal Algebra Class!"

- Balloony to Cloudy

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 went after they are eliminated pre-split 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 seen on-screen.

As of "Take the Tower", the EXIT is no longer used to send eliminated contestants to, and are sent to BRB instead via X|X's snap.

Appearance
Eternal Algebra Class consists of two parts within Four. The outside of the room is a dark and endless plane, with strange, blue tree-like growths with the shape of Four on top. This area is known as The Fourest. A door connects the Fourest 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 Four's desk, there is a to-do list presumably written by Four. The contents written on it are as follows:


 * thank Pin
 * get David
 * get 8-Ball
 * get Stapy
 * get Loser
 * get Roboty
 * do rejoins
 * KILL CLOCK

The last task that is written likely alludes to how Four quickly screeched at Clock in an earlier scene.

In the back of the room, there are two corkboards and a locked door. As of BFB 16, the door is boarded up and there is a sign taped to one of two cones guarding the door. The sign reads "STOP TRYING TO OPEN THIS DOOR". However, in "You Know Those Buttons Don't Do Anything, Right?", the barricades covering the door were removed by Liy, due to wanting to know what was behind it. The corkboard on the left has two papers each with computers drawn on them, as well as some small writing that cannot be read. Perhaps they are 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 corkboard on the right is labeled "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, likely suggesting that it is about X and Y positions and possibly even Z positions. Bracelety's project has the function $$y^4=1-x^4$$ written on it (which, when graphed, resembles a picture of Ice Cube), and Pencil's project has the equation $$A = \sqrt{3a^2}$$ written on it (when graphed, makes a V shape) Leafy's project, however, is rather mysterious. It has lots of pairs of numbers written on it, written large and clear. 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", the path that Spongy took avoiding the lasers in "Gardening Hero", and the path Puffball took to avoid cannonballs in "The Four is Lava".

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 photocopier/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", likely written by Bracelety. Near it, a page is pinned to the wall with the text "$$\div5\div6=0.83333333$$". 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 $$^3\sqrt{16777215+1}$$, 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.

In "The Escape from Four", the room is updated again to reflect Leafy's rejoin, and Dora, Firey Jr., and Match's eliminations. The photograph of Leafy in the "EXITORS" bulletin board is obscured by a photograph of Match. Firey Jr. and Dora's photographs are pinned to the side of the first nine eliminated contestants.

A shot of the room in this episode shows the back bulletin board on the right (formerly labeled "My Project") with additional papers pinned. One of Leafy's papers appears to be missing and is replaced with a blank piece of paper. Firey Jr.'s and one other contestant's project is pinned to the bulletin board, although it is unclear what the projects read.

Class activities
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 stuck on Question 4. She had also written the phrase "How can I show my work for this?" in question 1, seeing as how it's a very basic subtraction problem.

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 of 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 that have entered the EXIT
The contestants listed in the order they were eliminated.

Known seating chart
The Exitors appear to be seated based in the order that they were eliminated.

Trivia

 * Four refers to EXIT using multiple terms and euphemisms, such as "sleeping", going away, "getting poo-pooed", "getting zooped", "GOOD LUCK EVER THINKING HAPPILY AGAIN", "going away feeling empty inside" and "go bye-bye".
 * Leafy was the first 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. She didn't return to team Beep, but got placed on The Losers! instead. Loser and Spongy also left in BFB 16.
 * Before she rejoined, her seat was between Bracelety and Pencil.
 * This seat was eventually taken by Match.
 * With Leafy gone, there are no more Squashy Grapes in the EXIT.
 * 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 fool's 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 is 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 a 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 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 the back row to the front row. The fourth to sixth eliminated contestants sit in the middle row, etc.
 * The question "64-1", mentioned by Pencil, maybe a reference to her elimination, where the number of remaining contestants decreased from 64 to 63. Coincidently she was the person that was eliminated in that equation.
 * If one looks closely at the cameras, Four and the eliminated contestants can't be seen.
 * The EXIT is made in CGI and rendered with Blender.
 * Although there are windows, no land or other contestants can be seen outside.
 * The EXIT is fairly close to the Fourest, as seen in "The Four is Lava".
 * As of BFB 16, Dora is the last contestant to enter EXIT.
 * Due to too many people in the EXIT, Balloony and later eliminated contestants who were eliminated in the episodes after BFB 17 had to go to the Big Rotating Building instead.
 * The EXIT will no longer appear in BFB, but will appear in future episodes of TPOT.