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:
“I would like you to place 1 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 farmer earned?
[Hint: The following table may help you. What is the first square on which the king will place at least Rs 10 lakh?]
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: “I would like you to place 1 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 farmer earned

Solution:

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.

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.

We have to determine the money that the farmer has earned.

Given, a 8 × 8 grid.

Sum of first row = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷

= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128

= 255

Sum of second row = 2⁸ + 2⁹ + 210 + 2¹¹ + 2¹² + 2¹³ + 2¹⁴ + 2¹⁵

= 2⁸(2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)

= 256(255)

= 65280

Sum of third row = 2¹⁶ + 2¹⁷ + 2¹⁸ + 2¹⁹ + 2²⁰ + 2²¹ + 2²² + 2²³

= 2¹⁶((2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)

= 256 × 256 × 255

= 16711680 and so on

✦ Try This: (-5)⁻³ ÷ (-5)⁻⁷ = (-1/5)ˣ. Find x.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 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: “I would like you to place 1 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 farmer earned?

Summary:

The farmer earned 255 on the first row, 65280 on second row, 16711680 on third row and so on.

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