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Conditional Formatting 'Blocks' of cells

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I am wondering if it's possible to use a custom formula in conditional formatting to highlight a single 3x3 block of cells - rather than a single cell, an entire row/column, or the entire range - based on values within the cell.

I've fussed with it a bit but, as far as I've found, the only way I would be able to get it to work would be to create multiple rules for each different cell in the block. I can't imagine how much work that would be with the number of variations I might need. So I'm hoping there's a somewhat simpler solution that I'm missing.

I created a sample "chessboard" sheet to somewhat simplify and help illustrate what I'm trying to do:

And here are the parameters I'm trying to accomplish

Here's a link to the chessboard sheet

The formatting of the cells is just to keep it similar to my intended use in case that somehow acts as a variable in any potential solution.

Is this possible? Am I missing something or looking at it the wrong way?

I've been searching all day and I can't find any examples of anyone trying to do what I'm doing here... Go figure

Edit:Thank you to Eric for the workable solution to what it looks like I was asking, however my real intent is for the cells to change based on user input in the color and checkbox cells:

WHITE +☐ = White; BLACK+☐ = Black; WHITE +☑ = Yellow; BLACK+☑ = Purple

I've edited the sheet to clarify this better.


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