How do you efficiently count rectangles in grids?

By selecting distinct horizontal and vertical lines.

How can you handle counting rectangles in complex grid shapes?

Break down the grid into smaller sections.

To avoid double-counting rectangles.

Determine ways to choose horizontal and vertical lines.

Efficiently counting rectangles in grids involves selecting distinct pairs of horizontal and vertical lines to define each rectangle, simplifying the calculation process.
For complex shapes like L-shaped grids, breaking down the grid into smaller sections, calculating rectangles in each, and adjusting for overlaps is crucial to accurately determine the total number of rectangles.

How do you efficiently count rectangles in grids?
By selecting distinct horizontal and vertical lines.
What mathematical concept can simplify rectangle counting?
Binomial coefficients.
How can you handle counting rectangles in complex grid shapes?
Break down the grid into smaller sections.
What is the significance of selecting distinct lines in rectangle counting?
To avoid double-counting rectangles.
How can you calculate the total number of rectangles in a grid?
Determine ways to choose horizontal and vertical lines.

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The puzzle involves counting rectangles in two different grids, with 675 rectangles in the first grid and 900 in the second.
The key to counting rectangles efficiently lies in selecting pairs of distinct horizontal and vertical lines that uniquely define each rectangle.
To calculate the total number of rectangles in a grid, determine the number of ways to choose two distinct horizontal lines and two distinct vertical lines.
Utilize binomial coefficients to simplify the calculation process, such as 6 choose 2 for horizontal lines and 10 choose 2 for vertical lines.
For more complex shapes like an L-shaped grid, break down the grid into smaller sections, calculate the rectangles in each section, and adjust for overlapping areas to find the total number of rectangles.