AP or No AP?

Number Theory Level 2

From the set {1,2,3,...,n1,2,3,...,n}, 1010 numbers are removed such that there is no Arithmetic Progression of length 1111 among the numbers left in the set.

Find the smallest nn such that no matter which 1010 numbers are removed, there always is one Arithmetic Progression of length 1111.

Kaushik Maran by Kaushik Maran
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