While pootling around the arcane labyrinth of multi-dimensional sodalite, I encountered a combinatorial puzzle which seems of independent interest, and reasonably straightforward --- more than can be said for numerous other heffalump-traps lately encountered over the course of that tortuous expedition! Given n > 0 integer, evaluate the number f(n) of integer vectors P of length n such that 0 < P_(i+1) - P_i < n for all i , and (P_i - P_j) mod n /= 0 for all i /= j , and sum_i P_i = n(n-1)/2 . For example when n = 4 there are f(4) = 6 such vectors: [ 0, 1, 2, 3 ], [ -1, 1, 2, 4 ], [ -2, 1, 3, 4 ], [ -1, 0, 2, 5 ], [ -2, 0, 3, 5 ], [ -3, 0, 3, 6 ]. The explicit function f(n) is surprisingly simple; but the proof is not immediately obvious. Fred Lunnon