Question

# An 8&times;8 chessboard has a square cell (or box, like square a1) which measures &eta; inches on one side.

Complex numbers

An $$8\times8$$ chessboard has a square cell (or box, like square a1) which measures $$\beta$$ inches on one side.

Express the two possible moves of your knight in vector form with units in inches.

What are the distances of each possible move from your original position in inches?

What are their angles from the horizontal (x-axis)?

2021-07-22

This is applicable for every $$n\times n$$ square board.

The total number of squares for $$n\times n$$ square board can be calculated as

$$1^{2}+2^{2}+3^{2}+\cdots+n^{2}$$

So for a Chess Board with $$8\times8$$ squares total no.of squares

$$= 1^{2}+2^{2}+3^{2}+\cdots+8^{2} = 204$$

Thus there are 204 Squares in a $$8\times8$$ Chess Board.