Mind you, Tolkien wrote 'five' at the time just because 'five wizards' sounded good. He didn't invent the Blue Wizards until years later.
Indeed, early in the writing of Book V, four years later, he thought the Witch-King might be a renegade wizard.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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