Given a 100 by 100 square grid, what is the most number of 1 by 51 rectangles that we can cut out of it?
149
Hmmm. I get 100 + 49
wrong
To find the maximum number of 1 by 51 rectangles that can be cut out of a 100 by 100 square grid, we need to consider the dimensions of both the grid and the rectangle.
Let's start by analyzing the dimensions of the grid. The grid is 100 by 100, which means it has 100 rows and 100 columns.
Now, let's consider the dimensions of the rectangle. The rectangle has a width of 1 and a height of 51, meaning it has 1 row and 51 columns.
To cut out as many 1 by 51 rectangles as possible, we need to align the rectangles in such a way that they do not overlap and cover the maximum area of the grid.
Since the width of the rectangle is 1, we can place 100 rectangles along each row of the grid. However, because the height of the rectangle is 51, we can only fit 2 rectangles vertically in each column of the grid, as 51 multiplied by 2 equals 102.
Now, let's calculate the maximum number of rectangles that can be cut out:
Number of rectangles per row = Grid width / Rectangle width = 100 / 1 = 100
Number of rectangles per column = Grid height / Rectangle height = 100 / 51 ≈ 1.96 ≈ 2 (rounded)
To get the maximum number of rectangles, we take the minimum value between the number of rectangles per row and the number of rectangles per column.
Maximum number of rectangles = Minimum (Number of rectangles per row, Number of rectangles per column) = Minimum (100, 2) = 2
Therefore, the maximum number of 1 by 51 rectangles that can be cut out of a 100 by 100 square grid is 2.