# At what board does the white rooks stay at the beginning of the game?

## At what board does the white rooks stay at the beginning of the game?

Placement and movement The white rooks start on squares a1 and h1, while the black rooks start on a8 and h8. The rook moves horizontally or vertically, through any number of unoccupied squares (see diagram). As with captures by other pieces, the rook captures by occupying the square on which the enemy piece sits.

**How many pieces is a checkerboard?**

12 pieces

**How many squares are in an 8×8 checkerboard?**

Originally Answered: How many squares are in an 8×8 checkerboard? There are 64 (8 squared) 1×1 squares, 49 (7 squared) 2×2 squares, 36 3×3’s, 25 4×4’s, 16 5×5’s, 9 6×6’s, 4 7×7’s and one 8×8, for a total of 204.

### How many rectangles are in a 2×3 grid?

a 2×3 grid has 6 1×1 (2 * 3) squares and 2 2×2 (2 * 1) squares = 8. (we solved this above.) If you continue this you can easily see that a 2 x m grid has 2*m + 1*(m — 1) squares in it.

**How many rectangles are in a 5×5 grid?**

Count the number of rectangles which can be created starting with this square. There are five different rectangles with a height of 1, five different rectangles with a height of 2, which leads to 5 x 5, or 25 different rectangles starting with this square.

**How many squares are in a 7×7 grid?**

There are 64 1×1 squares and a single 8×8 square. For the 7×7 squares, they will leave one top or bottom row and one side column each. Thus, they each have to be stuck in one of the four corners. This means that there are four 7×7 squares.

## How many rectangles are in a 5×3 grid?

We have discussed counting number of squares in a n x m grid, Let us derive a formula for number of rectangles. If the grid is 1×1, there is 1 rectangle. If it grid is 3×1, there will be 3 + 2 + 1 = 6 rectangles.

**How many squares are in a 4×4 grid?**

After they have had a chance to think about and have yelled out some more answers ask them how many squares there are in a 1×1 grid (1) and in a 2×2 grid (the 4 small squares and the 1 big square = 5) and a 3×3 grid (9 small squares, 4 of the 2×2, and 1 big one = 14). So the total for a 4×4 is 16 + 9 + 4 + 1 = 30.

**How many squares are in a 9×9 grid?**

Number of squares of all sizes in a square grid n*n is sigma n^2 or n(n+1)(2*n+1)/6. 9*10*19/6 = 15*19 = 285.

### How many squares are in a 100×100 grid?

100 1×1 squares

**How many squares are in a 20×20 grid?**

Hint: How many 1×1 squares are there, how many 2×2? Answer: 2870. There is one 20×20, four 19×19, nine 18×18, sixteen 17×17, etc.