AP or No AP?

Number Theory Level 3

From the set {\(1,2,3,...,n\)}, \(10\) numbers are removed such that there is no Arithmetic Progression of length \(11\) among the numbers left in the set.

Find the smallest \(n\) such that no matter which \(10\) numbers are removed, there always is one Arithmetic Progression of length \(11\).