Question

Once upon a time a Brahimin went to an Arrogant King and asked him to give him some money to survive but he made joke of him, And this made him embarrassed. That's why Brahmin decided to take revenge. 
He asked The King to fulfill his wish and king agreed, but the brahmin demanded to take pledge that the king will satisfy his needs. King agreed, he thought that what a brahmin can take from him, just some money that's it. 

Brahmin Demanded money equivalent to the total number of boxes in a chess board. He asked them to give him money in multiple of two. 

for e.g. He will start from ₹ 1 from first box of chess in multiple of 2 in each successive box of chess. 
₹1 in first box, 2×1 = ₹2 from second box and 2 × 2 = ₹4 from third box and goes on to 64 boxes. 

Now, tell me, How much money that Brahmin will get, in Total ? 

Answer 1

It would be umm...

₹ 18,446,744,073,709,551,615

On the entire chessboard there would be 2^64 − 1
Rupees.





The problem may be solved using simple addition. With 64 squares on a chessboard, if the Number of rupees doubles on successive squares, then the sum of rupeess on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of ruppess equals 18,446,744,073,709,551,615 (the 64th Mersenne number), much higher than what most intuitively expect.

That means He is an owner of about 19 quantillion with no investment, Isn't it wicked?

Answer 2

HELLO THERE!!

The above question is indeed an interesting one!!

According to my knowledge,
The money that is to be given to the Brahmin will be calculated in GP series (Geometric Progression).

Why?

Note:
For 1st box, he will get Rs.1
For 2nd box, he will get Rs. 2 x 1 = Rs.2
For 3rd box, he will get Rs. 2 x 2 = Rs.4

The common ratio of the money that he gets after each step is the same.
Let the common ratio be r.

Common ratio of a GP series is calculated by dividing the second term by the first.

Hence, in this case,
$r = \frac{2}{1}$
So, r = 2.

Let the first term be a.
Since, for the first box, he gets Rs. 1,
a = 1.

Now we have to calculate the sum of this GP series. The resultant sum will denote the amount which he will receive.

Since the value of r is 2,
it means that r > 1.
n = 64.

So,refer to the picture to get the formula of the Sum of 64 terms (since there are 64 boxes in total) and the calculation....

So, the Brahmin shall get Rs. 18446744073709551615

I'm not sure about the answer; Calculation says that this is the right answer...
If you find any mistake, correct me.