Q1701 A school class consists entirely of twins: $2n^2 + 2n$ pairs of them, where $n \geq 2$. Including the teacher, there are $4n^2 + 4n + 1$ people in the class, so they can stand in a $2n + 1$ by $2n + 1$ square array. Prove that however they arrange themselves in this array, it will be possible to find $2n+1$ of the children (excluding the teacher) in such a way that no two of the chosen children are standing in the same row, no two are standing in the same column, and no two are twins.