Why don't n-1 for df in this scenario

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Simple statistics question, but can't figured out.

What is the critical value t* for constructing a 99%, percent confidence interval for a mean with 11 degrees of freedom?

My answer for this is 3.169 where df = 10 and two tails' value is 0.01

But the correct answer is 3.106 where df = 11.

I am confused why we don't minus 1 here for df.

Don't we df = n -1 where n is the sample size?