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John, you have done an excellent job. You won the first prize.

Is the above sentence acceptable?
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Actually, Teo, you make a good point. Idiomatically, we do say "You won first prize" or "You took first place."

When you put the article in there, it does sound like John won the first prize that was awarded that day, but not necessarily the prize that was first in importance.
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You need the, because we're talking about a specific prize, the first prize.
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Comments  
Yes, or you've won.
TeoJohn, you have done an excellent job. You won the first prize.

Is the above sentence acceptable?

Why use the definite article before "first prize"? I think the difinite article should be deleted.

 Marius Hancu's reply was promoted to an answer.
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 BarbaraPA's reply was promoted to an answer.