Shades of gray are created by combining the primary color inks. I do not use that printer, but if it has a two tone mode, black or white, then it may use just the black cartidge. However, don't count on that stroke of luck. That's how printers used to work.
Most modern printers will not print anything if a cartridge fault is present. They do this to protect the print head from damage from overheating when no ink flows throught it.
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