diff --git a/rlbench/tasks/place_cups.py b/rlbench/tasks/place_cups.py
index fd8c53838..d74c26239 100644
--- a/rlbench/tasks/place_cups.py
+++ b/rlbench/tasks/place_cups.py
@@ -1,10 +1,11 @@
+from itertools import combinations
 from typing import List, Tuple
 import numpy as np
 from pyrep.objects.dummy import Dummy
 from pyrep.objects.proximity_sensor import ProximitySensor
 from pyrep.objects.shape import Shape
 from rlbench.backend.conditions import DetectedCondition, NothingGrasped, \
-    OrConditions
+    OrConditions, ConditionSet
 from rlbench.backend.spawn_boundary import SpawnBoundary
 from rlbench.backend.task import Task
 
@@ -32,8 +33,12 @@ def init_episode(self, index: int) -> List[str]:
         self._index = index
         b = SpawnBoundary([self._cups_boundary])
         [b.sample(c, min_distance=0.10) for c in self._cups]
-        success_conditions = [NothingGrasped(self.robot.gripper)
-                              ] + self._on_peg_conditions[:index + 1]
+        # Descriptions specify a count, not particular cup identities.
+        success_conditions = [
+            NothingGrasped(self.robot.gripper),
+            OrConditions([ConditionSet(list(cups)) for cups in
+                          combinations(self._on_peg_conditions, index + 1)])
+        ]
         self.register_success_conditions(success_conditions)
         self.register_waypoint_ability_start(
             0, self._move_above_next_target)
diff --git a/tests/unit/test_place_cups_conditions.py b/tests/unit/test_place_cups_conditions.py
new file mode 100644
index 000000000..2f8e8c59e
--- /dev/null
+++ b/tests/unit/test_place_cups_conditions.py
@@ -0,0 +1,38 @@
+"""Count distinct cups rather than requiring an unmentioned cup-ID prefix."""
+import itertools
+import unittest
+from types import SimpleNamespace
+from unittest.mock import Mock, patch
+
+from rlbench.backend.conditions import DetectedCondition, OrConditions
+from rlbench.tasks.place_cups import PlaceCups
+
+
+class TestPlaceCupsConditions(unittest.TestCase):
+    def test_all_sensor_states_and_variations(self):
+        cups = [object() for _ in range(3)]
+        gripper = Mock()
+        task = PlaceCups(None, SimpleNamespace(gripper=gripper))
+        task._cups = cups
+        task._cups_boundary = object()
+        sensors = [Mock() for _ in range(3)]
+        task._on_peg_conditions = [OrConditions([
+            DetectedCondition(cup, sensor) for sensor in sensors
+        ]) for cup in cups]
+        with patch('rlbench.tasks.place_cups.SpawnBoundary'):
+            for variation in range(3):
+                task.init_episode(variation)
+                for bits in itertools.product((False, True), repeat=9):
+                    matrix = [bits[i * 3:(i + 1) * 3] for i in range(3)]
+                    for j, sensor in enumerate(sensors):
+                        sensor.is_detected.side_effect = (
+                            lambda cup, j=j: matrix[cups.index(cup)][j])
+                    for held in (False, True):
+                        gripper.get_grasped_objects.return_value = [cups[0]] if held else []
+                        expected = not held and sum(map(any, matrix)) >= variation + 1
+                        with self.subTest(variation=variation, bits=bits, held=held):
+                            self.assertEqual(bool(task.success()[0]), expected)
+
+
+if __name__ == '__main__':
+    unittest.main()