I will assume you mean that the tiles are 14 inches square and that the room is 18 ft by 33 ft.
18 ft is 216 inches, and 33 ft is 396 inches.
As a first approximation, the room is 85536 sq inches so dividing this by 14 squared, or 196. we get just over 436.4 squares. However, this is unlikely to be enough with cutting to fit. It's usual to start in the centre of the room and to lay as many full tiles as possible, then to cut tiles to fill in the borders. You'd need about 140 full tiles, depending on exactly where you start. The number of part tiles needed will then depend on whether they have a nap or not. I'd say you need at least another 21 to be sure.
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To determine the number of squares on a 15x15 grid, we need to consider squares of different sizes. There will be 15x15 = 225 individual squares of size 1x1. Additionally, there will be (15-1)x(15-1) = 14x14 = 196 squares of size 2x2. Continuing this pattern, there will be 225 + 196 + 169 + ... + 1 squares of different sizes, which can be calculated using the formula for the sum of squares. The total number of squares on a 15x15 grid would be 1^2 + 2^2 + 3^2 + ... + 15^2 = 1240 squares.
12 inches = 1 foot1 square yard = 9 square feet466 square yards = 4,194 square feet24" x 24" = 2' x 2' = 4 square feet4,194/4 = 1,0481/2 carpet squares
A 14 x 14 foot square is 196 square feet.
You can make three squares
There are 9 squares I can see 12 squares in an array of 2 * 4 squares