The answer is 2011. The question can be brute force.
An old math teacher of mine gave me this fun little problem: For each number n from 1 to 9, make 6 from three copies of n, using only basic-ish arithmetic and no other numbers.  For example, 2+2+2 = 6.  I will leave the rest as a puzzle for the reader.Precise statement of restrictions (enumerating these may give you a bit of a hint): You're allowed to use these operators: + - * / √ !I did this, and then I figured out that if you're allowed to use the floor function as well, you can fulfill this task for any n ≥ 1.  If [x] denotes the floor of x, then I'll demonstrate with 56:√56 is somewhat less than 8. √√56 is somewhat less than 3. √√√56 is somewhat less than 2.  Then [√√√56] = 1.  Thus, we can have: ([√√√56]+[√√√56]+[√√√56])! = 3! = 6.The expression to find "number of times you'll have to take square root of n" is slightly interesting: we want to take k square roots and end up with something less than 2, so n^(1/2^k)  log_2(log_2(n)).