Math Genius

Mathematics has little surprises that are designed to test and push your mental limits.
 If you're looking for a mathematical way to impress your friends and beguile your enemies, here's a good place to start.
The following 3 simple math problems prove outstandingly controversial among students of math, but are nonetheless facts.
Math Tricks

Math Genius in History

This is old math genius, math genius in history.
I do not know if the following is true, but someone attributed this to Hazrat Ali ibn Abi-Taalib (May Allah be pleased with him) as a Math Genius:
One Day a person came to Hazrat Ali (May Allah be pleased with him), thinking that people say "Ali is too smart;" I'll ask him such a tough question that he won't be able to answer and I'll embarrass him in front of all Arabs.

He asked, "Ali, can you tell me a number, that if we divide it by any number from 1-10 the answer will always come in the form of a whole number and not as a fraction." Ali Looked back at him and said, "Take the number of months in a year, multiply it with number of days in a month (30), and multiply that with the number of days in a week and you will have your answer." The person did not believe Ali. He checked the answer and found it was correct. The number was 12 x 30 x 7 = 2520

Math Facts

Most of you in high school have seen the quadratic equation, which tells you how to solve the degree 2 polynomial equation ax² + bx + c = 0.
solve a quadratic equation

But the story doesn’t end there. In the 1500s, mathematicians solved the cubic equation (degree 3), which is just one step up: ax³ + bx² + cx + d = 0. The corresponding solution is far more complicated:

qubic equation do you solve a quartic equation (degree 4): ax⁴ + bx³ + cx² + dx + e = 0?
At this point, the formula is absolutely ridiculous:

quartic formula

Now breathe a sigh of relief, because I’m not going to show you the formula for the next step up, the quintic equation (degree 5): ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0, because it doesn’t exist!
It’s not that we haven’t found it yet; we actually proved it’s impossible!

In fact, for any polynomial with degree 5 or higher, there is no solution in roots.

Math Tricks

Kaprekar Number 6174 Theory | The number 6174 is the only unchanged mysterious number discovered by Kaprekar's operation. Discover the mystery behind the 6174 loop by using any four digit number.

Kaprekar Number 6174 Theory
Step 1
Select any four digit number, but do not select the ones in which all the four digits are the same like 1111, 2222, ...
Step 2
Arrange the digits in decreasing order.
Step 3
Arrange the digits in increasing order.
Step 4
Subtract the smaller number from the larger number.
Step 5
Repeat the steps 2, 3 and 4 until you get 6174 in repetition.

Example 1
Step 1 :  4 digit number is 5620. 
Step 2 :  Arrange decreasing order : 6520 
Step 3 :  Arrange increasing order : 0256 
Step 4 :  Subtract the smaller number from the larger number : 6520 - 0256 = 6264 
Step 5 :  Take the final result and repeat the steps 2, 3, and 4 until you get the repetition of 6174. 

Example 2
6264 = 6642 - 2466 = 4176 
4176 = 7641 - 1467 = 6174 
6174 = 7641 - 1467 = 6174 

Have fun with this math trick and discover why all the 4 digit numbers on subtracting using the kaprekar operation reach to the mysterious number 6174.