The fixed +1/-4 offsets in get_courses only produced a collision-free
rotation for certain group counts; for n=9 (three groups per course) the
pairwise gaps collapsed and 9 pairs of groups met twice.
Replace it with a resolvable transversal design (_rotation_hosts): slots
form a k x 3 grid, each course is a parallel class partitioning all groups
into transversal tables of three, guaranteeing every pair meets at most
once for any n >= 9. n=3/6 are combinatorially impossible and fall back to
a degenerate same-row rotation that still satisfies the structural
invariants. Add a regression test asserting no pair meets more than once.
lars
e7bb0b9c69