Not a single one; not even one of something (used for emphasis).
From Old English 'nǽfre' (never one), contracted to 'ne'er a' and eventually 'nary.' It's an archaic or dialectal way of saying 'not one.'
Nary is a wonderful old-fashioned word that survives mainly in phrases like 'nary a soul'—it's how people emphasize complete absence before modern words like 'zero' or 'none' became common.
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