**Note from the admin :**

This is not a trick or an easy method to solve multiplication.It is just for those who really appreciate the beauty of mathematics.

*Also, strict action will be taken if he/she uses it on any other site,not even youtube.*

So, let’s get started :

If we want to multiply 12 X 12, we know that the answer is 144.

**Now, if we want to know a number such that, if we subtract it from 1212, our answer should be 144 ?**

The number
is **1068.**

Now,this blog is all about :

**how to find this number?**

If the first number (being multiplied) is 12, and the second number is P Q .

Then, the answer will be 1 2 P Q – 1 0 9-n 11-n.

Where n= P-1 Q + 1.

For example, if we want 12 X 13, then

Here, P=1,Q=3, so, n= 04 = 4.

Now,9-n = 9-4 = 5.

And, 11-n = 11-4 =7.

So, answer will be 1213 – 1057 = 156, and of course, 12X13 = 156 !!

**What about if the first number is 13
?**

Then,the number which we have to subtract is 1 1 8-n 12-2n.

So, if we want 13X18, then 1318 – 1 1 (8-9) (12-18).

Or, 1318-11(-1)(-6) which is 022 14

If we add the two middle terms, then our answer will be 234.

Now, for any number 1 t , we have the number to be subtracted as 1 t-2 f-n 1 g – tg,

Where f is such that the previous digit + f must equals to 9.

Where g = t-1.

If we want 14×16, then the number to be subtracted from 1416 is given as :

Here, P=1,Q=6,t = 4

So, n= 7,f=7,g=3.

The last digit is 13-3(7) = 13-21 = -8

The second last digit : 7-7 = 0

So, the answer is : 1416 – 1 2 0 -8 which is 0 2 1 1 4 ,

If we just add the two middle terms, our answer is : 224 ,which is correct.

Now, the main issue is to find the last term, please note that we can find the last term by the method given above or we can just multiply t and q.

Then, to obtain the second digit of the answer, we have to subtract the second digit of the number from p-1.

For example, if we want to multiply 15 and 16, then :

**What if the numbers do not start with 1 ?**

Will upload it soon !!!!