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Question 170

Long back in ancient times, a farmer saved the life of a king's daughter. The king decided to reward the farmer with whatever he wished. The farmer, who was a chess champion, made an unusal request
"would like you to place rupee on the first square of my chessboard . 2 rupees on the second square, 4 on the third square, 8 on the fourth square and so on, until you have covered all 64 squares. Each square should have twice as many rupees as the previous square ' The king thought this to be too less and asked the farmer to think of some better reward, but the farmer didn't agree.

How much money has the farme
r earned?

[Hint The following table may help you. What is the first square on which the king will place aleast 10 lakh?]


Solution

Given, a 8×8 grid.
Now, find the sum of each row,
e.g. 1st row =20+21+22+23+24+25+26+27=2552nd row=28+29+210+211+212+213+214+215=28(20+21+22+23+24+25+26+27)=28×255=255×256=652803rd row=216×255=16711680    [28=256 and 216=28×28=256×256 and so on]


Mathematics

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