Question 14
In plane, let be given an octagon $A_1A_2A_3A_4A_5A_6A_7A_8$ such that no three of its diagonals are concurrent. Each point of intersection of every two diagonals of the octagon is called a cross.
Consider the convex quadrilaterals whose vertices are vertices of the given octagon. Each such quadrilateral is called a subquadrilateral.
Find the least positive integer $n$ such that one can colour $n$ crosses so that for every $i, k \in \{1, 2, 3, 4, 5, 6, 7, 8\}$ and $i \ne k$, if we denote by $s(i, k)$ the number of
subquadrilaterals admitting $A_i, A_k$ as vertices and admitting a coloured cross as the point of intersection of the diagonals then the values $s(i, k)$ are all equal.
Consider the convex quadrilaterals whose vertices are vertices of the given octagon. Each such quadrilateral is called a subquadrilateral.
Find the least positive integer $n$ such that one can colour $n$ crosses so that for every $i, k \in \{1, 2, 3, 4, 5, 6, 7, 8\}$ and $i \ne k$, if we denote by $s(i, k)$ the number of
subquadrilaterals admitting $A_i, A_k$ as vertices and admitting a coloured cross as the point of intersection of the diagonals then the values $s(i, k)$ are all equal.