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I'm working on a Google Sheet and want to reformat all instances where the number in a cell is "2" and the color of the cell is pink. Is it possible to use information about cell formatting (here, e.g., color) in my IF function?

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No, IF function on its own does not understand colors. You will need either script or add-on for that. Also, you may try Conditional formatting where you can color cells based on values and the same logic can be used in IF formula:

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Google Sheets built-in functions doesn't return cell formatting attributes like borders, color, text formatting, etc.

One alternative is to use Conditional Formatting.

Another alternative is to use Google Apps Script either to create a custom function that returns the cell attributes of interest or even to do the "whole" job.

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