Let n \equal{} 2k \minus{} 1 where k≥6 is an integer. Let T be the set of all n\minus{}tuples (x1,x2,…,xn) where xi∈{0,1} \forall i \equal{} \{1,2, \ldots, n\} For x \equal{} (x_1, x_2, \ldots, x_n) \in T and y \equal{} (y_1, y_2, \ldots, y_n) \in T let d(x,y) denote the number of integers j with 1≤j≤n such that xi=xj, in particular d(x,x) \equal{} 0. Suppose that there exists a subset S of T with 2k elements that has the following property: Given any element x∈T, there is a unique element y∈S with d(x,y)≤3. Prove that n \equal{} 23. functioninductionalgebra unsolvedalgebra