Given a 100 by 100 square grid, what is the most number of 1 by 51 rectangles that we can cut out of it?
To find the maximum number of 1 by 51 rectangles that can be cut out of a 100 by 100 square grid, we can analyze the dimensions and divide both the width and the height by the corresponding value of the rectangle.
Since the rectangle has a width of 1, we can divide the width of the grid by 1. In this case, 100 divided by 1 is 100.
Similarly, dividing the height of the grid by 51, we get 100 divided by 51, which yields approximately 1.96.
Notice that we cannot have a fraction of a rectangle, so we need to consider the largest integer value we can obtain from dividing the two dimensions.
Since we obtained 100 when dividing the width by 1, and approximately 1 when dividing the height by 51, we can only fit 1 rectangle in the height of the grid.
Therefore, the maximum number of 1 by 51 rectangles that can be cut out of a 100 by 100 square grid is 1.