Checkerboard Problems
- Draw a line across a 4 x 5 checkerboard so that the maximum
number of regions are intersected. Extend to an m x n checkerboard.
- How many squares of any size are in an 8 x 8 checkerboard?
Extend to an m x n checkerboard.
- How many rectangles of any size on an m x n checkerboard?
- Given only the lattice points (points where four of the squares
meet), how many squares of any size can be found on a 5 x 5 grid?
For example,
- Extend to an m x n grid.
- Given only the lattice points of an n x m grid where n and
m are very large, can you draw a linethrough the grid which intersects
no lattice points, only one lattice point, only two lattice points?
Answer the same question for m and n both infinite.
- Make up your own problem or problems related to a checkerboard.
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