Question: Consider a blank m x n rectangular grid. Your goal is to shade in squares in the grid such that the following two restrictions are

Consider a blank m x n rectangular grid. Your goal is to shade in squares in the grid such that the following two restrictions are satisfied: No shaded squares are adjacent along an edge

All unshaded squares are connected along edges so that a continuous "path" can be found connecting any two unshaded squares For a specified grid size, what is the maximum number of squares that can be shaded following these restrictions?

I am in a Mathematical Reasoning class and have this problem due Friday. I have tried to complete it, but I am just going in circles. There are no notes from class on this problem - we are instructed to "try it."

For this problem, the unshaded "paths" cannot be broken. For example, you cannot have a checkerboard grid because the unshaded squares are cut off from each other. All unshaded squares must be connected by edges. There cannot be a "lone square" which is not connected to the others, or is connected by corners.

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