It's Not any Maths Trick , But a Miracle of Numbers which I Found by Mistake ( Timepass kar Raha tha )
Take a Calculator.
Add Numbers by line Diagonally with their own reverse . Ex. (159+951)=1110
Now do this for both diagonals and horizontal and vertical lines of numbers in calculator which passes through center you will get same answer i.e. 1110 .
- 159 + 951 = 1110
- 357 + 753 = 1110
- 258 + 852 = 1110
- 456 + 654 = 1110
This is not the real fun .
It is Here , In all above equation ( Cases ) , the common thing is middle term i.e. 5 . AND If you multiply term (5) by 2 , it is 10 both the digits of 10 is present at first and last digit of 1110 . AND If both the digits of 10 is added we get 1 , which is present in the middle part of 1110 .
Let's take it further ,
Add 123456789 and 987654321 you will get 1111111110 , Common Thing , Middle term is 5 again.
Amazing , let's take it even further
We done this trick for number line Passing through centre only . Now take number line which did not pass through centre ( i.e.5) :-
- 123 + 321 = 444
- 147 + 741 = 888
- 369 + 963 = 1332
- 789 + 987 = 1776
See Something , The Answer is Multiple of 444 , like 444*4=1776. The common thing in this is Middle Term only . Middle term is also getting multipled with same sequence 2468 .
Now ,
In First and Second Equation , If we multiply middle term by 2 we will get 4 and 8 , which is nothing but the first and last digits of 444 and 888.
In Third and Fourth Equation , If we Multiply middle term by 2 , we will get 12 and 16 , which is nothing but the first and last digit of 1332 and 1776 . And If we add both the digits 1+2=3 and 1+6=7 , this two numbers 3 and 7 are the middle terms of 1332 and 1776 .
Still Hungry ? ,
Let's Take Differences of all the above equations and see the Magic Once Again .
- All Horizontals
- 321 - 123 = 198
- 987 - 789 = 198
- 654 - 456 = 198
- All Verticals
- 741 - 147 = 594
- 852 - 258 = 594
- 963 - 369 = 594
- Diagonals
- 753 - 357 = 396
- 951 - 159 = 792
Notice , Some thing , all results are multiple of 198 . It works with triangles also like 351 - 153 = 198 .
I Found this while I was passing my time on Calculator and found this .