What is game theory? Which domains is it applied to?

What is game theory? Which domains is it applied to? by Naman Chakraborty

Answer by Naman Chakraborty:

Remember the 2014 Indian General Election Campaign?

While Congress and other opposing parties were busy trying to project Narendra Modi as a divisive political figure – He came up with a slogan:

Sabka Saath – Sabka Vikaas.

Loose Translation:
Along with everyone – Progress for everyone.

We all know the final result.

This is game theory.

Game Theory is the mathematics, economics or science of taking an action, after you’ve taken into account how other participants are expected to behave.

Generally, since more than one participant is involved in complex real world scenarios, you do not make a guess work and instead make use of the awesomely interesting algorithms and mathematical models of Game Theory.

It’s kind of like you as a kid pretending to want the Orange flavored ice cream instead of the Cola flavored one, secretly hoping that it makes your sibling choose Orange.

Remember, you can only apply Game Theory in case where the participants are rational decision makers (So you do not apply it on Pakistan…pliss).

Today, Game Theory is considered an important tool in many fields like diplomacy, town planning, marketing and warfare and has earned a total of 11 Nobel Prizes in Economics for its masters.

This guy is known as a father figure in Game Theory:

When he was a 22 years old student, he wrote a 28 page dissertation, with a lot of graphs and equations, basically explaining why one should always hit the second hottest woman in a bar, to increase the chances of getting a date (inference, not the conclusion) – He called it – The Nash Equilibrium[1].

44 years later, the Nobel Prize Committee finally got impressed and decided to give him the Nobel Prize in Economics, which made him kind of like the Brad Pitt of Mathematics, around the world – sadly, he was 67, happily married and suffering from advanced schizophrenia. He died two years ago, in a car accident.

Hollywood made a brilliant feature film based on the life of Nash, starring Russell Crowe, it’s called, A Beautiful Mind[2].

With a hope that this generates more interest in you to perhaps read more about the Game Theory. Thank you for reading, cheers and peace 🙂


[1] http://www.columbia.edu/~rs328/N…

[2] A Beautiful Mind (2001)

What is game theory? Which domains is it applied to?


Who are the top 10 Warriors in Ramayana and Mahabharata?

Who are the top 10 Warriors in Ramayana and Mahabharata? by Vignesh Saravanan

Answer by Vignesh Saravanan:

Firstly the answer is quite long,might be boring too read at your own risk…..

According to Hindu mythology there are 5 classes of warrior excellence.

  1. Rathi: A warrior capable of attacking 5,000 warriors simultaneously.
  2. Atirathi: A warrior capable of contending with 12 Rathi class warriors or 60,000
  3. Maharathi's: A warrior capable of fighting 12 Atirathi class warriors or 720,000
  4. Atimaharathi's: A warrior capable of fighting 12 Maharathi warriors simultaneously
  5. Mahamaharathi's: A warrior capable of fighting 24 Atimaharathi's simultaneously

Here is the list of warrior that I consider the top 10 based on the warrior classes and other powers they possess

For Ramayana,

There are a considerable amount of equally powerful warriors like Lava, Kusa, Parashurama, Kartavirya Arjuna etc during that era. But I have left such warriors out for various reasons .

10. Angada

Class : Atirathi

Race: Vanara(half man-half monkey)

Notable mention : He is Nephilim(Son of Vali)

Angada,the fierce son of vali,has killed many great warriors from Lanka, including,Ravana’s son, Narantaka, and Mahaparshva, chief general of Ravana’s army. Angada and his mother were the main reason for convincing Sugriva to help Lord Rama to find his wife,Sita. When he was sent to lanka for diplomatic reason where he was humiliated, he challanged the members of Ravan’s court to lift his leg from the ground at which everyone failed.

09. Atikaya

Class: Maharathi

Race: Rakshasas

Notable mention : Had an armor that can be pierced only by Brahmastra

Atikaya,the son of Ravana and the younger brother of Indrajit.Once upon a time when he infuriated Lord Shiva atop Mount Kailasha, the deity hurled his Trishula (divine trident) at Atikaya, but Atikaya caught the Trishula in mid air and folded his hands before the lord in a humble manner. Lord Shiva was pleased at seeing this, and benevolently blessed Atikaya with the secrets of archery and divine weapons. An invincible armor of Lord Brahma was granted to Atikaya, owing to which Lakshmana killed him using Brahmastra.

08. Jambavan

Class : Maharathi

Race : Rikshas( Were-bears)

Notable mention : He was created by Brahma himself to aid Rama.

Jambavan,the King of the Bears,has received a boon from Lord Rama that he would have a long life, and have the strength of ten million lions. It is he who makes Hanuman realize his immense capabilities and encourages him to fly across the ocean to search for Sita in Lanka.Several years later during Mahabharata era ,he even managed to put a tough fight with Lord Krishna.

07. Kumbhakarna

Class : Maharathi

Race : Rakshasas

Notable mention :He was massive colossus that 1000 elephants could walk over him.

Kumbhakarna, the gigantic brother of Ravana is a fearsome monsterous-Rakshasas who sleeps for six months at a stretch, rising for only one day and then returning to his slumber. Kumbhakarna can slay hundreds of warriors by the sweep of his hand or step of his foot. He injured Hanuman, and knocked Sugriva unconscious and took him prisoner, but was ultimately killed by Rama. When Ravana heard of his brother's death, he faints and proclaims that he is truly doomed.

06. Lakshmana

Class : Maharathi

Race : Human

Notable mention : He is a quarter manifest of Vishnu and avatar of Adi shesha.

Lakshmana,the quick-tempered brother of Lord Rama is as powerful and excellent a warrior as his brother, and slayed extremely powerful demons, including Atikaya and Indrajit.He also posses many celestial weapons.

05. Vali / Sugriva

Class : Maharathi

Race : Vanara

Notable mention: Vali- Demigod(Son of Indra)/Sugriva -Demigod(Son of Surya)

Though Vali didn’t fight in the war,he and his twin brother Sugriva were equally matched in power ,Vali outmatched him by his boon that he had received, according to which anyone who fought him in single-combat lost half his strength to Vali, thereby making Vali invulnerable to any enemy.This boon alone is enough to acknowledge the fact, when its comes to single-combat,Vali will be victorious if the enemy uses his brute strength alone.

04. Ravana

Class: Maharathi

Race: Rakshasas

Notable mention : King of Rakshasas and the grandson of Pulastya(one of Brahma’s Mind sons)

Ravana, a rakshasa is the king of Lanka. He was son of a sage named Vishrava and daitya princess Kaikes. After performing severe penance for ten thousand years he received a boon from the creator-god Brahma: he could henceforth not be killed by gods, demons, or spirits. He is portrayed as a powerful demon king who disturbs the penances of rishis . Vishnu incarnates as the human Rama to defeat him, thus circumventing the boon given by Brahma.

03. Lord Rama

Class: Maharathi

Race: Human

Notable mention: He is the seventh avatar of Lord Vishnu and the only one to posses Vaishnavastra other than Indrajit and Parashurama during this era.

Rama ,the seventh avatar of god Vishnu, he is the eldest and favourite son of Dasharatha, the king of Ayodhya and his Chief Queen, Kausalya.Rama single-handedly slays the 14,000 demon hordes of Khar (in one hour, according to the Ramayana), the demons Maricha and Subahu, Ravana's chief commander Prahasta and is responsible for the ultimate killing of Ravana himself.

02. Indrajit a.k.a Meghnadha

Class: Atimaharathi

Race: Rakshasas

Notable mention : Possessed all three ultimate weapons of Trimurti’s and many more celestial weapons, can spread darkness and ignorance among enemies which greatly empowered the might of the Rakshasas, Master of Sorcery and Archery

Meghnadha,the eldest son of demon king Ravana was an excellent warrior.He was given the name ‘Indrajit’ after defeating Indra, the king of Devas by Lord Brahma.He had a boon that no one could win him over a battle field if he had completed Yagna and boarded his celestial chariot.He coupled his supreme fighting skills with various stratagems to inflict heavy losses on Vanara army before his death. Indrajit is t one of the few warriors in hindu mythology who is in Atimaharathi class. I placed him second because of the fact that most celestial weapons have no effect on the number one

01. Hanuman

Class: Maharathi

Race: Vanara

Notable mention: : He is a Demi-god(Son of Vayu),Incarnation of Lord Shiva and the greatest devotee of Lord Rama

Hanuman,who belonged to a half-man half-monkey race was an invincible warrior. He, the son of a vanara king Kesari was the minister of Sugriva and was considered a formidable solider in the vanara army.Lord Rama has said that Hanuman can not even be defeat by him in a fight. Mostly importantly he played a major role in the battle by killing thousands of demons and reviving his fellow soldiers and his Lord Rama.

For Mahabharata,

As per Bhishma in Mahabaratha, there are three classes of warriors: Rathi, Atirathi and Maharathi. I have considered only warrior fought in kurukshetra war.

10. Bhima/Duryodhana

Class: Rathi(both were equal to 8 Rathi)

Both of them where equally skilled with mace and were equally powerful in their one on one.They were almost equal to Atirathi. However Bhima, being the half brother of Hanuman had learned a few tricks from him which helped him in the final battle.

09. Satyaki

Class: Atirathi

Satyaki was the greatest natural-born human warrior in the Mahabharata. He was taught by Arjuna.Everyone else who fought is either a demigod, nephilim, or son of some great sage, or perhaps born under extraordinary circumstances.He is regarded as almost equal of Arjuna. However had no knowledge of Chakravyuha.

08. Ashwatthama

Class: Maharathi

Ashwatthama had knowledge of some great weapons and ranks third in killing the most number of warriors in the war.He is the avatar of one of the eleven Rudras. He is cursed with immortality. He was born with a gem in his forehead which gives him power over all living beings lower than humans. This gem is supposed to protect him from attacks by ghosts, demons, poisonous insects, snakes, animals etc.He was also responsible for leading the night raid at the end of 18th day of the war and killing all the remaining Panchala army and sons of Pandavas.

07. Ghatotkacha (Night Form)

Class : Atirathi

He is a master Illusionist who can baffle almost all celestial weapons. Karna had to use one of the most powerful weapons in the world to take down this guy, and even then, he took an entire legion with him just by falling down on them.He killed in masses like hundreds and thousands in one blow.Infact when Ghatotkacha realized that he was going to die, that he assumed a gigantic size. When the huge body fell, it crushed one akshuhini of the Kaurava army.

06. Abhimanyu

Class : Maharathi

Abhimanyu is a consummate warrior almost equal to his father. When he enters the unbreakable Chakra vyuha, he holds the entire Kuru host, with Drona, Karna and hundreds of other heroic warriors, in addition to hundreds of thousands of foot soldiers at bay single-handedly. He is killed however, by deceit and a merciless and unlawful slaying while he is unarmed and without a chariot, by the Kauravas.

05. Bhagadatta

Class: Maharathi

Bhagadatta fought on the side of the Kauravas. He is very well known for his skill on his elephant.During the course of this battle, Bhagadatta fired an irresistible weapon called Vaishnavastra on Arjuna.However, Arjuna was saved from death by the timely intervention of Krishna. Krishna let himself to be cushion for that potent weapon, which turned into a garland and fell on Krishna. The Vaishnavastra was only known to Lord Krishna, Narakasura, Bhagadatta, Pradyumna and Parashurama during the Mahabharata age.

04. Drona

Class : Maharathi

Drona is a great master of Vedic military arts and almost every celestial weapon. He is invulnerable to any attack till he holds a weapon of any sort. This is the reason why the only way Pandavas could kill him was for him to throw down all weapons, which he does after hearing the death of his son. He also has great religious knowledge and wisdom. He becomes the second Kuru commander, and Arjuna is his favorite student. Drona's refused to teach Karna because Karna was not a prince, lays the foundation for the great Karna-Arjuna rivalry.

03. Arjuna

Class : Maharathi(Equal to 2 Maharathi)

He is one of the greatest archer on Earth and equal to Karna. He also pleased Lord Shiva who gave him his personal celestial weapon Pashupatastra, Lord Indra and others gods gave him all celestial weapons on his visit to heaven, he is also responsible for slaying the mighty demon race of Kalkaiya's, Puloma's and Nivatkavacha's. He is responsible for vanquishing Bhishma with help of Sikhandini, as well as exterminating an entire Akshauhini of warriors and Maharathas in one day, in addition to the armies of Samshaptakas, Trigartas and Narayanas – millions of soldiers and heroic warriors. He is also the protagonist in the great epic.Arjun held Gandiva, the personal bow of Lord Varuna.

02. Karna

Class :Maharathi(Equal to 2 Maharathi)

Karna,the son of Surya was born with kavach and kundal. They were armor of divine origins and could not be pierced with any kind of weapons.He sacrificed them for a great offence he received, the Shaktiastra that could slay immortals and it was used to kill Ghatotkacha who was on rampage on the 14th day of war . Karna's prowess is equal to Arjuna's in terms of Archery, however, he possessed strength and other war skills much more than Arjuna. There are many occasions where he over powered Arjuna.According to Krishna, Karna had all the qualities of the five Padavas – The Righteousness of Yudhisthira, Strength of Bhima, War Skills of Arjuna, Handsomeness of Nakula and Wisdom of Sahadeva. He had Vijaya bow the bow once held by Lord Shiva.


Class : Maharathi (Equall to 2 or 3 Maharathi)

Bhisma,the most consummate warrior trained by Parashurama, Bhisma is indestructible by any warrior when he lifts his weapons. Having defeated his preceptor himself, as well as all the kings of the earth, he is the Commander in Chief of the Kuru Army.He has a boon to die when he desired.Bhisma was well versed with tactical formations of the military in those days and only Drona, Krishna, Karna, & Arjuna could be compared to the vast knowledge that Bhishma possessed.

But there is warrior whose power is more than all of them in the above list and was in the battle field of Kurushetra war.

00. Lord Krishna

Class : Maharathi

Technically speaking Krishna didn’t really fight in the war but he is the one responsible for orchestrating the dead of all big shots.He was the eight incarnation of Maha Vishnu and possessed knowledge on all weapons. He is omnipotent,omnipresent and omniscient. His great power can only be matched by Trimurti’s.


And finally the list is over ,Sorry for the long answer….Actually writing this answers was really challenging since I had to compare a lot of warriors of equal standard and come out with the best. Some of them out there may not agree with my choice but this is my personal opinion. I neglected many powerful warriors like like Kartavirya Arjuna,Barbarica etc due to various factors one such great warrior is Parashurama,the sixth avatar of Vishnu who is belongs to timeline of both epics.He,being a Atimaharathi class warrior will be in the top 3 in both epics.

(Lord Parashurama fighting with Kartavirya Arjuna)

But I left him out owing to the fact that he didn’t fight the major wars of the epics.Same goes with other left out warriors.

*Disclaimer: The images I have added are just CG art.Since no one has ever seen any of this characters in real and only know them by their description from our ancient stories or arts,I took the liberty of adding the images that look close to their description.This image might not be the real image of the characters.

Source and references :

  1. Hindu mythological wars – Wikipedia
  2. Who according to you were the top 10 warriors during the time of the "Mahabharata" and how do you rank them from 1 to 10, except Lord Krishna?
  3. Who was the most powerful warrior in the Mahabharata?

Thanks for reading….Hope you enjoyed this…..

EDIT 1: Answers for FAQs:

  1. I could see many of the readers asking for the links of the above images . The above images are not from any particular site and they are just random images. You could search for them though but some of them are hard to get .
  2. Secondly, I could also see people asking for Barbarik in the list …Of course I agree he had a great offence , but I have neglected Barbarik for few reasons…One such reason is he didn’t fight in Kuruchetra war, moreover I believe that the characters in the list had enough tactics to counter his three arrows…I could justify this claim by saying that most of the characters from 00–09 had a lot of celestial weapons in their arsenal which they could use before Barbarik could launch all his three arrows (remember he had to launch all his 3 arrows to take his enemies out, but 1 divine arrow could take him down) …Moreover they knew at least one of the ultimate weapons i.e. Brahmastra, Pashupatastra and Vaishnavastra. Only Bhima and Duryodhana are defenseless against him but they are mace warriors, according to battle ethics Archers only fight with Archers right….When it comes to his father Ghatotkacha, he was a master of illusion and magic which made him immune to most celestial weapons..
  3. People also ask ‘ Why an Atimaharathi like Indrajit is placed below maharathi-Hanuman?’ (Thats because he is Lord Hanuman you genius)…Just kidding, now the fact….I accept Indrajit had a greater offense than Hanuman but when it comes to defense, Hanuman’s hands are raised far upper than that of Indrajit. Hanuman is immune to all celestial weapons and whats so cool is, not even the three ultimate weapons cannot harm him unless Hanuman himself gives in and plans to surrender to it.And this is reason for placing a lower class warrior above a upper class warrior.I hope this helps for that question.
  4. For people who ask ‘Wasn’t there a single Mahamaharathi in these two epics?’, The answers is ‘NO’ because only the Trimurti’s along with Ganesha and Devi Durga is considered to be of that class.Sometimes, Lord Karthikeyan is also referred to a Mahamaharathi.

Apart from this if you guys have any queries or suggestion feel free to comment friends…Thanks happy reading…

Who are the top 10 Warriors in Ramayana and Mahabharata?

What was Anudeep Nekkanti’s Competitive Programming strategy to become 35th in Global ranking, in just 6-7 months?

What was Anudeep Nekkanti's Competitive Programming strategy to become 35th in Global ranking, … by Anudeep Nekkanti

Answer by Anudeep Nekkanti:

What I did ?

Result ?

  • Became very good with C++ and STL
  • Got introduced to most Competitive programming KEYWORDS (like DP, maxflow, sets, hashing, etc)
  • Learned Standard Problems and Algorithms
  • Indenting code
  • Fast typing 😛

How ?
Before starting programming, I searched about how and where to start, many said "Learn an Algorithm, implement it, solve  problems related to it". I did not do it that way, If you know what algorithm to use you generally think in that direction and leave about correctness.  I did them problem by problem, easy to hard, I spent 1 – 4 hours on a problem.
I get the idea, I code it, Get it Accepted. (I used to test a lot, I always wanted to get AC on first go)

I do not get the idea, I save that problem and try it after a month again. If I still do not get them, then search for hints. If it clearly needed some algorithm which I never used then I first smile (? I could not only because I did not knew the algorithm 😛 ) and then start reading about that algorithm. TopCoder had tutorials of almost all common algorithms. This is where I did a BIG MISTAKE. I never cared about correctness or run-time analysis proof, I always learned how to solve the problem using that algorithm, I hardly learned about how the algorithm works. I feel bad about it now, but that is how I solved those problems then. I solved max-flow, convex hull, etc., problems using described algorithms but I did not UNDERSTAND those algorithms then.

Mistake: Once I started taking part in contests, I completely stopped practice.

35th in Global Ranking

  • CodeChef long contests are comparatively easy ( Which is good, You can learn a lot), you get a lot of time to think about a problem, search for resources. You only need KEYWORDS to search for similar problems.
  • I gave a lot of time for each contest. I used to solve 4 easy problems in 2-3 days, then take 5-6 days for other 3 problems.
  • CodeChef rating system is not good. It is highly Volatile.

If I am to start programming now, I would do it this way

  1. Solve 200 most solved problems on SPOJ, Problem by problem. In 2 months.
    (This will teach all standard problems, algorithms and implementation skills)
  2. Solve problems from CodeChef and CodeForces for 2 months.
    (This will teach variations, we can read others solutions and learn better ways. Skip easy problems)
  3. Solve problems from TopCoder for 2 months.
    (This will teach  Dynamic Programming. Div 1 500p)
  4. Check past ACM ICPC Regional's Problems
    (Great quality problems)

If I am to learn a new Algorithm now, I would do it this way

  1. Read it from at least 3-4 different sources.
  2. Understand correctness proof and run-time analysis.
    (This is very very important, you will know it only when you  deal with non standard  and hard problems)
  3. Question yourself on every step for correctness. Try to tweak the implementation.
  4. Check other implementations.

Final Note
Thought I became good in solving problems and had good rank. I later(Feb 13) realized that I learned it the wrong way. I then started learning again. I learned all the algorithms again this time gave importance to the algorithm itself, correctness proof and mathematical analysis. It is worth the time.

Lucy and the Flowers – Problem from December long contest, Try to solve it with suffix arrays. You can only if you understand suffix arrays and LCP completely.

I was able to solve a not-so-obvious medium level Max-Flow problem at ACM KGP Onsite only because I completely understood how the algorithm works. It was at 4 hour 25 minutes I got 5th problem accepted, then I read this problem and got it accepted 4 minutes before end. Learning the algorithm helped. Dot.

What was Anudeep Nekkanti's Competitive Programming strategy to become 35th in Global ranking, in just 6-7 months?

What are the most unusual things people have uploaded to GitHub?

What are the most unusual things people have uploaded to GitHub? by @NikolasKAMA

Answer by Nikolaos Kamarinakis:

There are quite a few bizarre projects one might come across on GitHub or anywhere else online. I mean it’s the Internet, right? Anything is to be expected.

Howbeit, some short scripts I read on GitHub some time ago really got to me.

The repository I am referring to can be found here. In brief, this absurdly lazy programmer attempted to automate his life by writing some ridiculous scripts:

I will not embark on what every one of these scripts ‘accomplished’; instead, you can read all about them on this short Foss Bytes article.

However, I will recount the one which I found the most ridiculously funny-the hangover script.

This piece of code sent a text message to the developer’s boss, containing an excuse to why he won’t be able to make it to work. It randomly picked an excuse from a pre-defined list (seen below) and used a service called Twilio to send the SMS using the programmer’s own phone number.

excuse = [
 'Locked out',
 'Pipes broke',
 'Food poisoning',
 'Not feeling well'

Ultimately, the boss received a message such as “Gonna work from home. Pipes broke” or "Gonna work from home. Food poisoning”.

Please, give this man a round of applause. He’s earned it.

What are the most unusual things people have uploaded to GitHub?

What are some awesome mathematics tricks?

What are some awesome mathematics tricks? by @Phantomgraphman

Answer by Philip Lloyd:

You will fool or at least, surprise, almost everybody with this wonderful trick!

Give a person a calculator to use.

Tell them to type any three digits (example 839)

Tell them to repeat the digits so they get a six figure number (839839)

Then you show them how incredibly quick you are!

Just glance at the number and say, “That number will divide exactly by 13″.

Tell them to do it.

Glance at this answer and say, “That number now will divide exactly by 11”.

Tell them to do it.

Finally say, “Your answer will now divide exactly by 7”.

Tell them to do it and to their surprise, the final answer will be the first three digits they thought of!!! (ie 839)

It is a good exercise to get people to prove this always works.

What are some awesome mathematics tricks?

What are the most famous unsolved mathematical equations?

What are the most famous unsolved mathematical equations? by @MaverickLin

Answer by Maverick Lin:

P = NP

This is one of the seven Millennium Prize Problems in mathematics. The discoverer of the solution of any one of the seven problems will be awarded a $1 million prize. This problem is notorious in Computer Science.

The Short Description

P is a set of relatively easy problems.

NP is a set of relatively very hard problems.

P = NP implies that all hard problems actually have very easy solutions.

The Long Description

This will take a while to fully explain, so try to bear with me if you want.

Much of CS is obsessed by how long does it take to execute an algorithm. Below is a chart of algorithmic complexity- it is usually described as a function of n, or the number of elements the algorithm has to manipulate.

The P stands for polynomial time. Polynomial time means that the complexity of the algorithm is O([math]n^k[/math])- basically cubic or above in the chart. So P is the set of problems that are solved in polynomial time. Algorithms that run in polynomial time are usually considered “good”.

NP stands for nondeterministic polynomial time. NP is the set of problems whose solutions can be verified in polynomial time. But the time spent solving the problem initially is undetermined- as far as we know, solving those take exponential time. In the picture above, the line that divides cubic and exponential is the “bad” line. Exponential time or factorial complexity is generally not good.

So does “P = NP” can be converted into, “If the solution to a problem can be verified in polynomial time, can the solution be initially found in polynomial time?”


The implications of P=NP are enormous.

If P=NP, then every hard NP problem would contain a hidden shortcut, which would allow computers to quickly find solutions to them.

If P != NP, then no shortcut exists and computers’ problem-solving capabilities will be always limited.

One practical example is cryptography. Computers’ inability to efficiently factor huge composite numbers form the cornerstone of modern cryptography- RSA public-key cryptosystem being the prime example (prime, get it?).

If you discovered that P=NP, you could essentially crack all the cryptosystems in the world. You would get access to all the bank accounts, government secrets (NSA), nuclear launch codes, anything.

As our Discrete Structures professor said, if you solve P=NP, don't go claim the $1 million prize. Bring it to him and you guys can rule the world together.

Edit: As per request, I am here to provide an example of P and NP. A simple example would be multiplication.

It’s a P problem to solve n * k- or 33 * 81 = 2,673. Bam. Done.

But it’s a NP problem to find the specific factors of 2,673- namely n and k. Why?

Because you can easily verify that 33*81 is 2,673, but solving for n and k given the product (2,673) is NP- n and k could be a wide range of numbers- 1 and 2,673, 3 and 891, etc…

Once the numbers get really really big, it will take exponential time to find the right factors.

Edit 2: As some have mentioned, I have missed some important details in an attempt to simplify the P=NP concept. The explanation above is barebones and minimum- think of it as a very basic primer or introduction to P=NP. In order to truly understand it, please consult more detailed sources. Cheers.

What are the most famous unsolved mathematical equations?

What do math geeks like about math?

What do math geeks like about math? by Brandon Ross

Answer by Brandon Ross:

Imagine you found a magic wand, covered in dust, in the bottom of a wardrobe of some aging wizard. It looks rather plain. You hold it in your fingers, and wobble it up and down.

But you’re caught in the act! The old man snatches it right from your hand.

“What does it do?” you ask.

He’s surprised. Your curiosity is rewarded.

“It holds great power. If you say the magic words in the right order, the wand may grant you your desires.”

He holds it in his hand. He pauses, and smiles at you.

“Do you want to learn this power?”

You nod.

The old man chuckles. Of course you do. But he warns you, “Any power can be wielded for good or evil. And mistakes? Mistakes can have terrible consequences.”

You do not fully understand. So, he explains the scope of the wand’s power.

With it, you could drop a giant boulder on your worst enemies. Even hurl it over their high castle walls.

Or you could prevent a village from starving. You might slow disease–even cure it. You might bring back people from the brink of death.

You could send a message to nearly anyone on the Earth. Sowing discord or bringing harmony. The wand could even tell you how to find these people. And, when you arrive there, you could understand the unknown tongues of foreigners.

You could have all of human knowledge at your beck and call. You would have the power to freeze an instant in time. And recall it, whenever you wish. You could conjure light without fire. Songs without singers.

You will know the substance from which all life and all things are made. You could build a tower straight into the air—high as a mountain—made of stone, glass, or metal. You could breathe underneath the oceans. You could soar through the sky like a bird. Or you could escape the Earth completely. You could visit the moon. Or travel to distant worlds that no human has ever visited. The moon, planets, and stars, you will understand their motion in the skies.

You could peer back in time and listen to the very first echoes of the universe's creation. And you could see into the future–long past your own death–and see the eventual demise of every far-flung star in the night sky. With that knowledge, you could unleash the power of a star and destroy entire cities in fire. Or, you could shackle that power, and give those people light and heat and water for generations.

None of these things would be beyond your understanding. You will see the order in all things. And the wildness coursing underneath all of it that—so far—has escaped all attempts to be tamed. And there is no answer to where this power has come from. It is wholly indifferent to you, to us, and to life. And yet we are all controlled by it—every moment of every day—whether we understand it or not.

You are curious. How does something so powerful escape our eyes? How can what this old man says be true? You want to know.

He continues. And if the material world becomes too small or too boring, there is more. You can conjure new realities. Things that have never existed. And will never exist. Where the laws of space and time bend to your whim.

He laughs.

And you will see that even those impossible worlds. They hold great power here in our own. You will see the fundamental magic words—that every beginner learns from the first day—still hold mysteries and power that no one can yet explain.

He is becoming excited himself. But he stops.

He tells you, no doubt, this wand you found in the bottom of his wardrobe wields a sublime, awe-inspiring power. Few mortal humans who will ever live and breathe will ever understand its true potential. Even the masters—who devote their entire lives to its study—know they are not far from humble beginners.

Rightfully, he cautions you that this power can take years to understand. Near everyone could use it. But most who study it would quit. They are too impatient. Minds too closed. Too little imagination. Too arrogant to learn from their mistakes.

He pauses.

“Are you sure that is something you are ready for?”

You nod, awkwardly. You secretly doubt yourself. He holds out the wand.

“Good. First, we will begin with the rules of addition.”

It is not magic. Through the study and application of mathematics, humans have obtained the power to do all of these things.

To most people, math is doing things with numbers. To math geeks, math is about relationships. Relationships are everywhere, between everything.

What do math geeks like about math?