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Prove That 2+2 = 5

blog author name

We’re on
That’s a nice way to start, Jonny
Are you such a dreamer
To put the world to rights?
I’ll stay home forever
Where two and two always makes a five!

Who hasn’t heard this amazing number from Radio head? The makers of this song were quite sure that two and two make a five.When did this become a popular question? Well, the credit goes to the film

Two & Two (2011 film) which made it a popular debate.

However, when I applied the same logic in my Maths exam, as a kid, my professor marked it wrong. I felt deceived, to be honest. Ever since, I have always wished of proving that grumpy professor wrong and I am glad I have finally found few way out!

Has your professor also forced you to believe that 2 + 2 = 4?

It’s time to prove him wrong!

After all you are a Small Einstein, who has the liberty to challenge even the axioms.

 It’s finally that moment when you can proudly tell him how

2 + 2 = 5

Wondering how? Grab a bowl of nachos as you scroll through the top six ways to prove this seemingly impossible equation.

Method 1:

First, let us solve this strange problem with the simplest possible method.

Let us assume:
0 = 0

Now “0” can result from the subtraction of one number with itself. So, let us assume that the two figures at L.H.S. and R.H.S. are 4, and 10.

Such that…. 4 – 4 = 10 – 10

Where, 4 can be written as 2*2

And 10 can be written as 2*5

Solving the equation further we get,

=> 2²-2² = 2×5 – 2×5

=> (2 – 2)(2 + 2) = 5(2 – 2)

Cancelling (2–2) from both sides we get

=> 2 + 2 = 5 (Hence proved)

Think this method was too plain to convince your professor? Are you looking for something crisper? Don’t worry, have a look at the next method.

Well, its good to be a choosy friend who will not believe in anything that the other friend says.

So for those choosy friends of ours, who are not satisfied with the above logic, we have a second answer.

Method 2:

Let’s now try to solve this problem by using a different method. How about tossing in some fractions to make the struggle look more serious?

Let us assume:

-20 = -20 ———- (1)

Where 20 can also be written as:

=> 16 – 36 and

=> 25 – 45

Now, placing these values in equation (1) we get:

=> 16 – 36 = 25 – 45

Which can also be written as:

=> 42 – 4 x 9 + 81/4 = 52 – 5 x 9 + 81/4

=> 42 – (2 x 4 x 9/2) + (9/2)2 = 52 – (2 x 5 x 9/2) + (9/2)2

=> (4 – 9/2)2 = (5 – 9/2)2

=> (4 – 9/2) = (5 – 9/2)

=> 4 = 5

Which eventually proves:

=> 2 + 2 = 5 (Hence Proved)

Well, even Pythagoras was condemned by
few, for saying that the earth is round. It is always good to refer to a new
method to prove yourself. So here goes method 3.

Challenging Mathematical Conventions: Two Equals Five

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Method 3:

Let us now relate this problem with a real-life example.

According to the given data:

 2 + 2=5


4 = 5

Let us suppose you have 4 chocolates and you gave all of them to poor children. Now you have 0 chocolates. When represented mathematically, you can write it as :

=> 4 – 4 = 0

Now, consider your friend has 5 oranges, and he also gives all of them to those children. He also ends up having nothing left with him. Mathematically:

=> 5 – 5 = 0

We can write

=> 0 = 0

=> 4 – 4 = 5 – 5

This can also be written as:

=> 4(1–1) =5(1–1)

=> 4=5((1–1)/(1–1))

=> 4 = 5


=> 2 + 2 = 5


=> 2+2=2+2+1


=> 2+2+1=2+2

Though this method proves that 2 + 2 = 5 but it’s not one of my favorites. So, I thought of adding some more spice to the problem. And when I say spice, I mean geometry. After all, things are always better understood pictorial representation, isn’t it?

Some people are not convinced by digits. So get convinced in angles with Method 4

Method 4:

Any geometry lovers out there? Here’s the geometrical solution to prove our unusual problem.

Let us suppose, there’s a triangle with AB = 4, AC = 5 and BC = 3.

Construct the angle bisector of ∠A and the perpendicular bisector of segment B.C.

Now, in the constructed figure:

AB = 4

AC = 5

So, the angle bisector and perpendicular bisector are not parallel. Hence, they intersect at a point O. Drop perpendiculars OR and OQ to sides A.B. and A.C., respectively. Form segments O.B. and O.C.

Case 1:

AO = AO by reflexivity,

∠RAO = ∠QAO   (AO is an angle bisector)

∠ARO = ∠AQO    (both are right angles)

 By A.A.S. congruence, ΔARO ≅ ΔAQO.

Consequently by CPCTC, AR = AQ and RO = OQ. ——-(1)

Case 2:

OD = OD by reflexivity,

∠ODB = ∠ODC   (both are right angles)

BD = DC           (OD bisects BC)

By S.A.S. congruence, ΔODB ≅ ΔODC.

Therefore, by CPCTC, O.B. = O.C. ——-(2)

Since we have proved that

R.O. = OQ ———-(1)

OB = OC ———-(2)

Also, since ∠O.R.B. and ∠O.Q.C. are both right angles, the hypotenuse-leg theorem for congruence implies ΔORB ≅ ΔOQC. Therefore, by CPCTC, B.R. = Q.C. —————(3)

We have shown that AR = AQ and BR = QC. Therefore, AB = AR + RB = AQ + QC = AC.

 In other words, 4 = 5,

 Thus, 2 + 2 = 5.

What? Is it too complex to be understood? Well, I loved it because I love geometry. However, I still have a surprise for those who didn’t like this method much. Wondering what it may be? Read on.

So, that’s how you prove 2 + 2 = 5. Wasn’t that easy?.

 I bet your professor would give you an accolade for proving him wrong! You are going to be his new favourite for sure!

Even if the solution may be wrong but this high level of logic will surely take your professor or teachers aback.

Method 5 (A bit funny):

This was how one of our friends made the equation true. DONT try it.

In his words…

“There were 2 boys trying to snatch 2 mangoes each from a friend of mine who had 5 mangoes.

I had been on bad terms with my friends .

I asked all three of them to fight over and whoever wins, would get the 4 mangoes.

My friend kept 5 mangoes on the ground and started fighting.

The three fought amongst themselves for quite long.

I reported my teacher that they were fighting. My teacher made them kneel down in front of the class and I was enjoying all the 5 mangoes.”

So I got 2 boys willing to get 2 mangoes each from my friend to get me 5 mangoes in total.”

Well, you would think it is a programming joke till you go through it.

Method 6:

You are going to love this last method, especially if you are a programming aficionado. 

Yes! You can solve this using a simple and easy code as well. All you have to do is, type these few lines of code, compile it and see for yourself that 2+2=5.

$ cat test.c

#include <stdio.h>

int main() {

int a = 3;

int b = 3;

// aren’t we supposed to add 2 and 2 ??/

a = 2;

b = 2;

printf(“%d\n”, a + b);

return 0;


$ gcc -W -Wall -trigraphs test2.c 2>/dev/null

$ ./a.out


So, that’s how you prove 2 + 2 = 5. Wasn’t that easy? I bet your professor would give you an accolade for proving him wrong! You are going to be his new favourite for sure!

Not just this, you can know the solution to other, more complex problems that tickle your brain. All you have to do is connect with us at

With, you can create unique, high level logic for more complex problems that tickle your brain.

All you have to do is connect with us at and get a different view of subjects.

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Hi, I am Ethan, a nerd by nature, a data scientist by profession and, a gadget lover at heart. Thanks for stopping by and sparing a few minutes to know me. I would like to let you know, apart from being a Maths lover and a tech freak I have a fetish for English writing. I am into everything that spells maths, technology, and essays. I have an experience of 10 years as a data scientist and that of 5 years as a freelance English essay writer at I like sharing my experiences with people, which further makes me an occasional blogger. 

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