Image text: Handy exam trick: when you know the answer but not the correct derivation, derive blindly forward from the givens and backward from the answer, and join the chains once the equations start looking similar. Sometimes the graders don't notice the seam.

Alright, this math equation only works because 9 is the square of 3, but this is fun none the less.

3 x 9 = 3 x the square root of 81 (the square root of 81 is 9).

That also equals 81 divided by 3 and then he solves the division by hand to get 27.

This is obviously not the way you solve the problem, but he uses handy math tricks like turning a square root into a division symbol to attempt to trick the math grader as he mentions in the image text.

Image text: Statistics suggest that there should be tons of alien encounter stories, and in practice there are tons of alien encounter stories. This is known as Fermi's Lack-of-a-Paradox.

This obviously is a made-up equation for the comic which is a spin off or reference to the Drake Equation which was previously referenced in this xkcd comic as well. The Drake Equation is an equation devised to calculate the number of extraterrestrial civilizations in our galaxy.

Here's the variable names:

WP = World Population

CR = Crazy

MI = Misinterpreted

TK = Tell _?

F0 = Immediate friends

F1 = Next level friends

DT = Details

AU = Audience

Fermi's Paradox is the contradiction between the high estimation of extraterrestrial life in the universe outside of earth and the lack of hard evidence of such life.  As you can see, the image text represents the lack of a paradox because the assumption and the actual facts are exactly the same.

Image text: The typical internet user (who wants to share) has an IQ of 147 and a 9-inch penis. Well, better than the reverse, I guess.

Let's start at the top.  The first search is from the song "99 Bottles of Beer on the Wall" in which every line is the same except the song starts at 99 and goes until the end at 1 bottle of beer on the wall.

The next six are self explanatory: number of boyfriends, grade level, penis size, bra cup size, age without having a boyfriend and number of glasses a day of water.

The next graph is a reference to Star Trek: The Next Generation in which Captain Picard is tortured when asked how many lights are behind the interrogator.  There are 4 lights, but Picard is tortured when he answers four.  The torturer wants Picard to admit there are 5.  This has turned into an internet meme, of course.

The next graph is a reference to the Jay-Z song "99 Problems" in which the chorus is: "I got 99 problems, but a bitch ain't one".

The last graph is a graph of people googling what they consider their IQ number of google results for each IQ number.  The image text references the high point on both the IQ and Penis graphs.

Image text: The Strong Collatz Conjecture states that this holds for any set of obsessively-hand-applied rules.

The Collatz Conjecture is a undecided or unsolved mathematical conjecture in which you have to do just as the comic says.  However, the comic takes it one step further since this conjecture is unsolved, you can keep working on it (by hand) obsessively until you do not have any friends any more.  Unless those friends want to come over and do math equations and conjectures by hand with you.

Image text: You want me to pick up waffle cones? Oh, right, for the wine. One sec, let me just derive your son's credit card number and I'll be on my way.

The principle of explosion means that if you assume that something is both true and untrue at the same time, then you can prove any conclusion.  Usually, someone would prove that something is true or false, but in the comic, the principle is used to derive a phone number and a credit card number.  The joke in the comic is taking the mathematical logic to the next level to make a joke about the first character's mom.

The equation in the third frame is the typical notation for a principle of explosion equation.  It means "P and Not P".  P represents some statement such as "the sky is blue".  So, the equation is: "The sky is blue and the sky is NOT blue."  From that premise, you can prove anything.  In the comic, you can even prove a phone number or credit card number.

Image text: I suppose that's more accurately a hare dryer.

Moose and Squirrel is a reference to the Rocky and Bullwinkle series of cartoons.

Longcat is a internet meme from pictures of cats all stretched out that make them look very tall (or long).

Mouse riding Bicycle is a reference to Ralph S. Mouse, a series of novels by Beverly Cleary.

The image text is a pun on the Rabbit with a hair dryer frame.

Legolas is a reference to the character by the same name in the Lord of the Rings trilogy of books and movies.

Knight is a chess reference as the tracks move just like the knight piece in chess.

The two "Kid with" frames are a reference to Calvin and Hobbes.

Prius is a reference to current events in which the car Toyota Prius's pedals have malfunctioned causing accidents.

The final frame is the Higgs Boson which is an elementary particle they are attempting to find evidence of in the Large Hadron Collider.

Anyone know what the Bobcat on a Pogo Stick is a reference to?  That's the only one I can't get.

Image text:  Sci-fi has energy weapons because otherwise the people like me who watch it get distracted counting shots.

Here's the full quote from Dirty Harry (a movie about a San Francisco cop who lives a bit outside of the rules to get the job done):

I know what you're thinking. "Did he fire six shots or only five?" Well, to tell you the truth, in all this excitement I kind of lost track myself. But being as this is a .44 Magnum, the most powerful handgun in the world, and would blow your head clean off, you've got to ask yourself one question: Do I feel lucky? Well, do ya, punk?

Rain Man is a movie about two brothers, one who is autistic played by Dustin Hoffman, the other played by Tom Cruise.

In the case of this comic, the person on the ground is autistic, so he has no trouble counting the bullets from Dirty Harry's gun.

Because of his counting skill, "Rain Man" is able to thwart Dirty Harry's intimidation's effect.

Image text: The contents of any one panel are dependent on the contents of every panel including itself. The graph of panel dependencies is complete and bidirectional, and each node has a loop. The mouseover text has two hundred and forty-two characters.

This is a comic, like the name, that describes itself.  However, as the image text explains, the contents are dependent on themselves and the other data.

The first frame is a pie chart of the black and white percentages of the whole comic strip.  If more black or white is added to any frame in the comic, the pie chart will change.

If the pie chart changes, the graph in frame 2 will change, which will cause the pie chart to change again and so on and so forth.

The third frame is an infinite loop of the comic.  If you look hard you can see the comic again and again in the last frame.

Image text: Or the pressure at the Earth's core will rise slightly.

Dimensional analysis is a tool to better understand the properties of items using an equation the helps to convert between different units of measure.  In this case, the comic says that the units check out.

Planck energy is a system energy made up of Planck units.

The pressure at the earth's core is over 3.5 million times atmospheric pressure.

Prius's gas mileage (as tested by the EPA) is 51 highway / 48 city.

The smallest width of the English Channel is 21 miles between Dover, England and Calais, France.

The image text is a continuation of the teacher's comments from the comic.

Image text: I mean, what's more likely -- that I have uncovered fundamental flaws in this field that no one in it has ever thought about, or that I need to read a little more?  Hint: it's the one that involves less work.

This comic is a discussion between two characters, the main character and the Philosophy major who has a goatee.  The image text is an additional comment by the character which the goatee.

The character with the goatee is suggesting that the people of science like the main character are holding firmly to their belief of the theory of special relativity.

This is a stereotypical representation of people such as Philosophy majors who thumb their noses at Phyics majors or other scientific ideas, which thinking that they always have the answers and have thought of a new idea that has never been thought of before.  This is referenced in the image text.