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Advanced MathQ&A LibraryA King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 2121 ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)How many grains of wheat should be placed on square 2121 ?nothinggrainsHow many total grains of wheat should be on the board after the the grains of wheat have been placed on square 2121 ?nothinggrainsWhat is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 2121 ?nothingpounds(Round to the nearest tenth as needed.)Question

Asked Mar 26, 2020

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A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square

21

21 ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)

How many grains of wheat should be placed on square

21

21 ?

nothing

grains

How many total grains of wheat should be on the board after the the grains of wheat have been placed on square

21

21 ?

nothing

grains

What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square

21

21 ?

nothing

pounds

(Round to the nearest tenth as needed.)

Step 1

A King in ancient times agreed to reward the inventor of chess with **one grain of wheat** on the **first of the 64 squares of a chess board.** On the **second square** the King would place **two grains of wheat**, on the **third square** he would place **four grains of wheat**, and on the **fourth square **he would place **e****ight grains of wheat.**

If the amount of wheat is doubled in this way on each of the remaining squares, then the corresponding number of grains of wheat and number of squares will be as follows.

Step 2

So, number of grains of wheat should be** placed on square 21** is 2^{20} = **1048576.**

Assume that each grain of wheat weighs 1/7000 pound.

And their **total weight** in pounds will be, (1/7000)*1048576 =149.79657 ≈ **149.79 pound**.

Step 3

Now, we need to find how many total grains of wheat should be on the board after the grains of wheat have been placed on square 21.

The above number is a very big number.

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