diff --git a/py/aoc2022/day16.py b/py/aoc2022/day16.py
index fe5f6af..268b612 100644
--- a/py/aoc2022/day16.py
+++ b/py/aoc2022/day16.py
@@ -3,7 +3,6 @@
 """
 
 import heapq
-import itertools
 import math
 import re
 from collections import defaultdict
@@ -117,28 +116,35 @@ def _solve(lines, num_agents, total_time):
             continue
 
         for delta, moves_by_agent in moves_by_time.items():
-            for size in range(1, num_agents + 1):
-                for combo in itertools.combinations(moves_by_agent.items(), size):
-                    indices = [i for i, _ in combo]
-                    for valves in itertools.product(*(valves for _, valves in combo)):
-                        if len(set(valves)) != size:
-                            continue
-                        new_rooms = [
-                            (room, age + delta + 1) for room, age in state.rooms
-                        ]
-                        for i, valve in zip(indices, valves):
-                            new_rooms[i] = valve, 0
-                        rate = sum(graph[valve][0] for valve in valves)
-                        new_state = _State(
-                            rooms=tuple(sorted(new_rooms)),
-                            valves=state.valves - set(valve for valve in valves),
-                            flow=state.flow + rate,
-                            total=state.total + state.flow * (delta + 1),
-                            time=state.time - delta - 1,
-                        )
-                        heapq.heappush(
-                            heap, (-estimate - rate * new_state.time, new_state)
-                        )
+            indices = [None] * num_agents
+            while True:
+                for i, index in enumerate(indices):
+                    index = 0 if index is None else index + 1
+                    if index < len(moves_by_agent[i]):
+                        indices[i] = index
+                        break
+                    indices[i] = None
+                else:
+                    break
+                valves = [
+                    (i, moves_by_agent[i][index])
+                    for i, index in enumerate(indices)
+                    if index is not None
+                ]
+                if len(valves) != len(set(valve for _, valve in valves)):
+                    continue
+                new_rooms = [(room, age + delta + 1) for room, age in state.rooms]
+                for i, valve in valves:
+                    new_rooms[i] = valve, 0
+                rate = sum(graph[valve][0] for _, valve in valves)
+                new_state = _State(
+                    rooms=tuple(sorted(new_rooms)),
+                    valves=state.valves - set(valve for _, valve in valves),
+                    flow=state.flow + rate,
+                    total=state.total + state.flow * (delta + 1),
+                    time=state.time - delta - 1,
+                )
+                heapq.heappush(heap, (-estimate - rate * new_state.time, new_state))
 
     return max_seen