diff --git a/CLAUDE.md b/CLAUDE.md
index 7f3529f..b9ad59a 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -30,7 +30,7 @@ The pipeline (see `src/tatami/tatami_masterplan.py` `__main__` block) is:
    - Splits participants into `hosts` (one per group, `len(participants)//6` groups of 3 courses each) and `semi_hosts` (non-hosting members assigned round-robin into existing groups), ranked by each participant's `get_after_party_time` (kitchen size penalty + distance to after-party).
    - Reduces the full distance matrix to just host-to-host distances (`reduce_distance_matrix`), adding each host's kitchen-size penalty into their row.
    - Runs `run_simulated_annealing` / `simulated_annealing` (Boltzmann-style annealing over `itertools.permutations` of group order — note this is brute-force over all permutations per iteration, so it only scales to a small number of groups) to find a low-travel-time ordering of groups.
-   - `assign_courses` assigns each group a course (starter/main/dessert cycling) and, via `get_courses`, determines which other groups host it for each course (offsets of `+1` and `-4` mod total groups — this fixed relationship is what defines the dinner-rotation topology).
+   - `assign_courses` assigns each group a course (starter/main/dessert cycling) and, via `get_courses`, determines which other groups host it for each course. The rotation is a resolvable "Latin-square"/transversal design (`_rotation_hosts`): slots form a `k x 3` grid (`k = n // 3` groups per course), each course is a parallel class partitioning all groups into transversal tables of three (one starter/main/dessert each), so for any `n >= 9` no two groups ever meet more than once. `n = 3`/`6` are combinatorially impossible and fall back to a degenerate same-row rotation. (This replaced an earlier fixed `+1`/`-4` cyclic offset that produced repeat meetings for group counts like 9.)
 4. `get_masterplan` returns two lists of plain dicts (`group.dict()`, `participant.dict()`) suitable for serialization; `compute_masterplan_groups` returns the live `Group`/`Participant` objects, which is what the `Plan`/sheet export step needs (`.hosts`, `.get_guests(...)`).
 5. **Wrap in a `Plan` and save** (`src/tatami/plan.py`) — `__main__` bundles the computed `groups` + `after_party_group` with the event config (`course_times`, `organizer_contacts`, `info_text`, `spreadsheet_id`) into a `Plan` and calls `plan.save(PLAN_FILE)`. On the next invocation, if that file exists, `Plan.load()` reads it back instead of recomputing — this is the save/reload/edit path: hand-edit `masterplan.json` (move a member between groups, change a course, fill in `spreadsheet_id`, ...) and rerun to pick up the edit without hitting the Routes API again.
 6. **Export to Google Sheets (optional)** — if the loaded/built `Plan.spreadsheet_id` is set, `__main__` calls `sheets_export.export_masterplan_to_sheet` to populate a pre-existing, pre-shared spreadsheet with an Overview tab and one tab per group. This is opt-in and never sends anything directly to participants — the organizer still shares the sheet link manually.
diff --git a/src/tatami/tatami_masterplan.py b/src/tatami/tatami_masterplan.py
index 7f00c17..48a4dd2 100644
--- a/src/tatami/tatami_masterplan.py
+++ b/src/tatami/tatami_masterplan.py
@@ -1,3 +1,4 @@
+from functools import lru_cache
 from pathlib import Path
 
 from tatami.classes import Participant, Group, Course
@@ -205,15 +206,68 @@ def simulated_annealing(
     return best
 
 
+# The rotation is a resolvable "Latin-square" / transversal design rather than a
+# fixed cyclic offset. Slots are laid out as a k x 3 grid: slot ``i`` cooks course
+# ``i % 3`` (starter/main/dessert) and sits in row ``i // 3``, where ``k = n // 3``
+# is the number of groups per course. Each course is one "parallel class" that
+# partitions all n groups into k dinner tables of three; every table is a
+# transversal (exactly one starter, one main, one dessert group), so no two groups
+# that cook the same course ever share a table.
+#
+# Table ``a`` of the class for course ``c`` is
+#     {S_a, M_{a + p[c]}, D_{a + q[c]}}   (row indices mod k)
+# where S/M/D are the starter/main/dessert groups. Two groups meet at most once iff
+# the three ``p`` values are distinct, the three ``q`` values are distinct, and the
+# three ``q - p`` values are distinct (mod k) -- these guard S-M, S-D and M-D
+# repeats respectively. ``p = (0, 1, 2)``, ``q = (0, 2, 1)`` satisfies all three for
+# every ``k >= 3`` (the values 0, 1, k-1 are distinct there), which covers every
+# real event size. ``k < 3`` (n = 3 or 6) cannot be made collision-free at all -- a
+# group would have to meet more distinct groups than exist -- so we fall back to a
+# degenerate same-row rotation (``p = q = 0``) that still satisfies every structural
+# invariant (see ``tests/test_routing.py``) even though tables then repeat.
+_COURSE_OFFSETS_P = (0, 1, 2)
+_COURSE_OFFSETS_Q = (0, 2, 1)
+
+
+@lru_cache(maxsize=None)
+def _rotation_hosts(total_meetings: int) -> tuple[tuple[int, int, int], ...]:
+    """Precompute, per slot, the (starter, main, dessert) host slots it dines at.
+
+    Returns a tuple indexed by slot; entry ``i`` is the three host slots the group
+    in slot ``i`` visits, ordered starter -> main -> dessert. The group is always
+    its own host for the course it cooks, so ``i`` appears in its own entry.
+    """
+    k = total_meetings // 3
+    if k < 3:
+        p = q = (0, 0, 0)
+    else:
+        p, q = _COURSE_OFFSETS_P, _COURSE_OFFSETS_Q
+
+    def slot(course: int, row: int) -> int:
+        return 3 * (row % k) + course
+
+    hosts: list[list[int]] = [[-1, -1, -1] for _ in range(total_meetings)]
+    for course in range(3):  # each course is one parallel class
+        for table in range(k):
+            members = (
+                slot(0, table),
+                slot(1, table + p[course]),
+                slot(2, table + q[course]),
+            )
+            host = members[
+                course
+            ]  # the class for course `course` is hosted by its course-`course` member
+            for member in members:
+                hosts[member][course] = host
+    return tuple((h[0], h[1], h[2]) for h in hosts)
+
+
 def get_courses(
     group_index: int,
     total_meetings: int,
-):
-    a = group_index
-    b = (group_index + 1) % total_meetings
-    c = (group_index - 4) % total_meetings
-    order = sorted((a, b, c), key=lambda x: x % 3)
-    return order
+) -> tuple[int, int, int]:
+    """The three host slots (starter, main, dessert order) that ``group_index`` visits."""
+    return _rotation_hosts(total_meetings)[group_index]
 
 
 def fast_total_time(distance_matrix: np.ndarray, solution: list[int]) -> float:
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 0413c6c..8c7b764 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -73,6 +73,20 @@ class TestGetCourses:
             assert len(guests) == 3
             assert {g % 3 for g in guests} == {0, 1, 2}
 
+    @pytest.mark.parametrize("n", [n for n in GROUP_COUNTS if n >= 9])
+    def test_no_two_groups_meet_more_than_once(self, n):
+        # The whole point of the Latin-square rotation: for n >= 9 (>= 3 groups per
+        # course) every pair of groups shares a table at most once across the evening.
+        # (n = 3 and 6 are combinatorially impossible and deliberately excluded.)
+        hosts_of = {i: set(get_courses(i, n)) for i in range(n)}
+        meetings = Counter()
+        for host in range(n):
+            guests = sorted(g for g in range(n) if host in hosts_of[g])
+            for a, b in itertools.combinations(guests, 2):
+                meetings[(a, b)] += 1
+        repeats = {pair: c for pair, c in meetings.items() if c > 1}
+        assert repeats == {}, f"pairs meeting more than once: {repeats}"
+
 
 class TestFastTotalTime:
     def test_matches_hand_computed_value_n3(self):