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# Chess Board

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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

2828​? 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 28?

How many total grains of wheat should be on the board after the grains of wheat have been placed on square 28​?

What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 28​?

Sep 17, 2019

#1
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On square 1 you have: 1

On square 2 you have: 2 or 2^(2 -1) =2 grains

On square 3 you have: 2^(3-1) =2^2 = 4 grains

On square 4 you have: 2^(4-1) =2^3 = 8 grains........and so on.

On square 28 you have: 2^(28-1) =2^27 =134,217,728 grains

Total numbers of grains on the board is just: (2^28) - 1 = 268,435,456 - 1 =268,435,455 grains.

The total weight of ALL grains of the board is:268,435,455 x 1 / 7,000 =38,347.92 or ~38,348 pounds

38,348 pounds / 2,000 pounds =~19.2 short tons!.

Sep 17, 2019

#1
+1

On square 1 you have: 1

On square 2 you have: 2 or 2^(2 -1) =2 grains

On square 3 you have: 2^(3-1) =2^2 = 4 grains

On square 4 you have: 2^(4-1) =2^3 = 8 grains........and so on.

On square 28 you have: 2^(28-1) =2^27 =134,217,728 grains

Total numbers of grains on the board is just: (2^28) - 1 = 268,435,456 - 1 =268,435,455 grains.

The total weight of ALL grains of the board is:268,435,455 x 1 / 7,000 =38,347.92 or ~38,348 pounds

38,348 pounds / 2,000 pounds =~19.2 short tons!.

Guest Sep 17, 2019