 Solution

Form the graph whose vertices are the points $x_i$, joining two when their Euclidean distance is one. Two distinct points have at most two common unit-distance neighbours, because two unit circles intersect in at most two points. The graph is therefore $K_{3,2}$-free. Part (c) bounds its unordered edges by $2n^{3/2}$, so the number of ordered unit-distance pairs is at most