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Andrew [12]
3 years ago
14

There are 8 rows and 8 columns, or 64 squares

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

Complete Question:

There are 8 rows and 8 columns, or 64 squares on a chessboard.

Suppose you place 1 penny on Row 1 Column A,

2 pennies on Row 1 Column B,

4 pennies on Row 1 Column C, and so on …

Determine the number of pennies in Row 1

Determine the number of pennies on the entire chessboard?

Answer:

255 in the first row

18,446,744,073,709,551,615 in the entire board

Step-by-step explanation:

Given

Rows = 8

Columns = 8

Solving (a): Number of pennies in first row

The question is an illustration of geometric sequence which follows

1,2,4....

Where

a =1 --- The first term

Calculate the common ratio, r

r = \frac{T_2}{T_1} = \frac{4}{2} = 2

The number of pennies in the first row will be calculated using sum of n terms of a GP.

S_n = \frac{a(r^n - 1)}{n - 1}

Since, the first row has 8 columns, then

n = 8

Substitute 8 for n, 2 for r and 1 for a in S_n = \frac{a(r^n - 1)}{r - 1}

S_8 = \frac{1 * (2^8 - 1)}{2 - 1}

S_8 = \frac{1 * (256 - 1)}{1}

S_8 = \frac{1 * 255}{1}

S_8 = 255

Solving (b): The entire board has 64 cells.

So:

n = 64

Substitute 64 for n, 2 for r and 1 for a in S_n = \frac{a(r^n - 1)}{r - 1}

S_{64} = \frac{1 * (2^{64} - 1)}{2 -1}

S_{64} = \frac{(2^{64} - 1)}{1}

S_{64} = \frac{(18,446,744,073,709,551,616 - 1)}{1}

S_{64} = \frac{18,446,744,073,709,551,615}{1}

S_{64} = 18,446,744,073,709,551,615

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