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Is there an equation for this? Like y = f(x) where y is your choice of gray and x is your color. Maybe you can empirically find “f” by fitting randomly created “x” with the resulting “y”.
If “f” can be approximated and maybe there’s something special about it so that you can find the inverse. Otherwise, you could always just generate a bunch of “x*” again, feed through “f”, and see whether the output “y*” matches your chosen gray.