diff --git a/examples/python/BUILD.bazel b/examples/python/BUILD.bazel
index 4a82eb9555..452ad05a6a 100644
--- a/examples/python/BUILD.bazel
+++ b/examples/python/BUILD.bazel
@@ -54,6 +54,8 @@ code_sample_test_arg_py(
     suffix = "salbp_20_1",
 )
 
+code_sample_py("maximize_combinations_sat")
+
 code_sample_py("maze_escape_sat")
 
 code_sample_py("no_wait_baking_scheduling_sat")
diff --git a/examples/python/clustering_sat.py b/examples/python/clustering_sat.py
index 86754e5cd6..14701b3801 100644
--- a/examples/python/clustering_sat.py
+++ b/examples/python/clustering_sat.py
@@ -65,7 +65,7 @@ distance_matrix = [
 ]
 
 
-def clustering_sat():
+def clustering_sat() -> None:
     """Entry point of the program."""
     num_nodes = len(distance_matrix)
     print("Num nodes =", num_nodes)
diff --git a/examples/python/cryptarithm_sat.py b/examples/python/cryptarithm_sat.py
index 083e89e3d0..39e98e5e0f 100644
--- a/examples/python/cryptarithm_sat.py
+++ b/examples/python/cryptarithm_sat.py
@@ -19,7 +19,7 @@ from absl import app
 from ortools.sat.python import cp_model
 
 
-def send_more_money():
+def send_more_money() -> None:
     """solve the cryptarithmic puzzle SEND+MORE=MONEY."""
     model = cp_model.CpModel()
 
@@ -74,7 +74,7 @@ def send_more_money():
     print("y:", solver.value(y))
 
 
-def main(_):
+def main(_) -> None:
     send_more_money()
 
 
diff --git a/examples/python/flexible_job_shop_sat.py b/examples/python/flexible_job_shop_sat.py
index b69a9fb0a4..7aa76932f4 100644
--- a/examples/python/flexible_job_shop_sat.py
+++ b/examples/python/flexible_job_shop_sat.py
@@ -46,7 +46,7 @@ class SolutionPrinter(cp_model.CpSolverSolutionCallback):
         self.__solution_count += 1
 
 
-def flexible_jobshop():
+def flexible_jobshop() -> None:
     """solve a small flexible jobshop problem."""
     # Data part.
     jobs = [  # task = (processing_time, machine_id)
diff --git a/examples/python/gate_scheduling_sat.py b/examples/python/gate_scheduling_sat.py
index ecf9d0fc03..6b46dbe41e 100644
--- a/examples/python/gate_scheduling_sat.py
+++ b/examples/python/gate_scheduling_sat.py
@@ -29,7 +29,7 @@ from ortools.sat.colab import visualization
 from ortools.sat.python import cp_model
 
 
-def main(_):
+def main(_) -> None:
     """Solves the gate scheduling problem."""
     model = cp_model.CpModel()
 
diff --git a/examples/python/golomb8.py b/examples/python/golomb8.py
index c648bf93dd..427f20f293 100755
--- a/examples/python/golomb8.py
+++ b/examples/python/golomb8.py
@@ -30,7 +30,7 @@ from ortools.constraint_solver import pywrapcp
 # pylint: disable=g-explicit-bool-comparison
 
 
-def main(_):
+def main(_) -> None:
     # Create the solver.
     solver = pywrapcp.Solver("golomb ruler")
 
diff --git a/examples/python/golomb_sat.py b/examples/python/golomb_sat.py
index 43ca39f03c..dec429b31d 100644
--- a/examples/python/golomb_sat.py
+++ b/examples/python/golomb_sat.py
@@ -38,7 +38,7 @@ _PARAMS = flags.DEFINE_string(
 )
 
 
-def solve_golomb_ruler(order: int, params: str):
+def solve_golomb_ruler(order: int, params: str) -> None:
     """Solve the Golomb ruler problem."""
     # Create the model.
     model = cp_model.CpModel()
diff --git a/examples/python/hidato_sat.py b/examples/python/hidato_sat.py
index cd20c50650..360276f7e4 100755
--- a/examples/python/hidato_sat.py
+++ b/examples/python/hidato_sat.py
@@ -147,7 +147,7 @@ def build_puzzle(problem: int) -> Union[None, list[list[int]]]:
     return puzzle
 
 
-def solve_hidato(puzzle: list[list[int]], index: int):
+def solve_hidato(puzzle: list[list[int]], index: int) -> None:
     """solve the given hidato table."""
     # Create the model.
     model = cp_model.CpModel()
diff --git a/examples/python/jobshop_ft06_distance_sat.py b/examples/python/jobshop_ft06_distance_sat.py
index 60ce5be641..430c241e47 100755
--- a/examples/python/jobshop_ft06_distance_sat.py
+++ b/examples/python/jobshop_ft06_distance_sat.py
@@ -36,7 +36,7 @@ def distance_between_jobs(x: int, y: int) -> int:
     return abs(x - y)
 
 
-def jobshop_ft06_distance():
+def jobshop_ft06_distance() -> None:
     """Solves the ft06 jobshop with distances between tasks."""
     # Creates the model.
     model = cp_model.CpModel()
diff --git a/examples/python/jobshop_with_maintenance_sat.py b/examples/python/jobshop_with_maintenance_sat.py
index 778e826194..e42a4bba5e 100644
--- a/examples/python/jobshop_with_maintenance_sat.py
+++ b/examples/python/jobshop_with_maintenance_sat.py
@@ -36,7 +36,7 @@ class SolutionPrinter(cp_model.CpSolverSolutionCallback):
         self.__solution_count += 1
 
 
-def jobshop_with_maintenance():
+def jobshop_with_maintenance() -> None:
     """Solves a jobshop with maintenance on one machine."""
     # Create the model.
     model = cp_model.CpModel()
diff --git a/examples/python/knapsack_2d_sat.py b/examples/python/knapsack_2d_sat.py
index b9b8521905..9adaa83f52 100644
--- a/examples/python/knapsack_2d_sat.py
+++ b/examples/python/knapsack_2d_sat.py
@@ -71,7 +71,9 @@ def build_data() -> tuple[pd.Series, int, int]:
     return (data, max_height, max_width)
 
 
-def solve_with_duplicate_items(data: pd.Series, max_height: int, max_width: int):
+def solve_with_duplicate_items(
+    data: pd.Series, max_height: int, max_width: int
+) -> None:
     """solve the problem by building 2 items (rotated or not) for each item."""
     # Derived data (expanded to individual items).
     data_widths = data["width"].to_numpy()
diff --git a/examples/python/line_balancing_sat.py b/examples/python/line_balancing_sat.py
index af97d80a2c..e2db9543e8 100644
--- a/examples/python/line_balancing_sat.py
+++ b/examples/python/line_balancing_sat.py
@@ -115,7 +115,7 @@ def read_model(filename):
     return model
 
 
-def print_stats(model):
+def print_stats(model) -> None:
     print("Model Statistics")
     for key, value in model.items():
         print(f"  - {key}: {value}")
@@ -183,7 +183,7 @@ def solve_model_greedily(model):
     return assignment
 
 
-def solve_boolean_model(model, hint):
+def solve_boolean_model(model, hint) -> None:
     """solve the given model."""
 
     print("Solving using the Boolean model")
diff --git a/examples/python/maximize_combinations_sat.py b/examples/python/maximize_combinations_sat.py
new file mode 100644
index 0000000000..2667b03b00
--- /dev/null
+++ b/examples/python/maximize_combinations_sat.py
@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+# Copyright 2010-2024 Google LLC
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Maximize the number of valid combinations of Boolean variables."""
+
+from typing import Sequence
+from absl import app
+
+from ortools.sat.python import cp_model
+
+
+def maximize_combinations_sat() -> None:
+    """Maximize the number of valid combinations of Boolean variables."""
+    model = cp_model.CpModel()
+    cards: list[cp_model.IntVar] = [
+        model.new_bool_var("card1"),
+        model.new_bool_var("card2"),
+        model.new_bool_var("card3"),
+        model.new_bool_var("card4"),
+    ]
+
+    combos: list[list[cp_model.IntVar]] = [
+        [cards[0], cards[1]],
+        [cards[0], cards[2]],
+        [cards[1], cards[3]],
+        [cards[0], cards[2], cards[3]],
+    ]
+
+    deck_size: int = 3
+    model.add(sum(cards) == deck_size)
+
+    valid_combos: list[cp_model.IntVar] = []
+    for combination in combos:
+        is_valid = model.new_bool_var("")
+
+        # All true implies is_valid.
+        model.add_bool_and(is_valid).only_enforce_if(combination)
+
+        # is_valid implies all true.
+        for literal in combination:
+            model.add_implication(is_valid, literal)
+        valid_combos.append(is_valid)
+
+    model.maximize(sum(valid_combos))
+
+    solver = cp_model.CpSolver()
+    solver.parameters.log_search_progress = True
+    status = solver.solve(model)
+
+    if status == cp_model.OPTIMAL:
+        print(
+            "chosen cards:",
+            [card.name for card in cards if solver.boolean_value(card)],
+        )
+
+
+def main(argv: Sequence[str]) -> None:
+    if len(argv) > 1:
+        raise app.UsageError("Too many command-line arguments.")
+    maximize_combinations_sat()
+
+
+if __name__ == "__main__":
+    app.run(main)
diff --git a/examples/python/maze_escape_sat.py b/examples/python/maze_escape_sat.py
index 833cdfe926..e4aac1870a 100644
--- a/examples/python/maze_escape_sat.py
+++ b/examples/python/maze_escape_sat.py
@@ -35,7 +35,9 @@ _PARAMS = flags.DEFINE_string(
 )
 
 
-def add_neighbor(size, x, y, z, dx, dy, dz, model, index_map, position_to_rank, arcs):
+def add_neighbor(
+    size, x, y, z, dx, dy, dz, model, index_map, position_to_rank, arcs
+) -> None:
     """Checks if the neighbor is valid, and adds it to the model."""
     if (
         x + dx < 0
@@ -55,7 +57,7 @@ def add_neighbor(size, x, y, z, dx, dy, dz, model, index_map, position_to_rank,
     arcs.append((before_index, after_index, move_literal))
 
 
-def escape_the_maze(params, output_proto):
+def escape_the_maze(params, output_proto) -> None:
     """Escapes the maze."""
     size = 4
     boxes = [(0, 1, 0), (2, 0, 1), (1, 3, 1), (3, 1, 3)]
diff --git a/examples/python/no_wait_baking_scheduling_sat.py b/examples/python/no_wait_baking_scheduling_sat.py
index 3031aa19f4..1bd1cd775b 100644
--- a/examples/python/no_wait_baking_scheduling_sat.py
+++ b/examples/python/no_wait_baking_scheduling_sat.py
@@ -21,7 +21,8 @@ We are scheduling a full day of baking:
 """
 
 import collections
-from typing import Sequence
+from typing import List, Sequence, Tuple
+
 from absl import app
 from absl import flags
 
@@ -124,7 +125,7 @@ class Order:
         self.quantity = quantity
 
 
-def set_up_data():
+def set_up_data() -> Tuple[List[Recipe], List[Resource], List[Order]]:
     """Set up the bakery problem data."""
 
     # Recipes.
@@ -193,7 +194,9 @@ def set_up_data():
     return recipes, resources, orders
 
 
-def solve_with_cp_sat(recipes, resources, orders):
+def solve_with_cp_sat(
+    recipes: List[Recipe], resources: List[Resource], orders: List[Order]
+) -> None:
     """Build the optimization model, and solve the problem."""
 
     model = cp_model.CpModel()
diff --git a/examples/python/pell_equation_sat.py b/examples/python/pell_equation_sat.py
index 09d12c50c0..29f3df5467 100644
--- a/examples/python/pell_equation_sat.py
+++ b/examples/python/pell_equation_sat.py
@@ -25,7 +25,7 @@ _COEFF = flags.DEFINE_integer("coeff", 1, "The Pell equation coefficient.")
 _MAX_VALUE = flags.DEFINE_integer("max_value", 5000_000, "The maximum value.")
 
 
-def solve_pell(coeff: int, max_value: int):
+def solve_pell(coeff: int, max_value: int) -> None:
     """Solves Pell's equation x^2 - coeff * y^2 = 1."""
     model = cp_model.CpModel()
 
diff --git a/examples/python/spread_robots_sat.py b/examples/python/spread_robots_sat.py
index 835e9c23f2..1d7f9d4513 100644
--- a/examples/python/spread_robots_sat.py
+++ b/examples/python/spread_robots_sat.py
@@ -33,7 +33,7 @@ _PARAMS = flags.DEFINE_string(
 )
 
 
-def spread_robots(num_robots: int, room_size: int, params: str):
+def spread_robots(num_robots: int, room_size: int, params: str) -> None:
     """Optimize robots placement."""
     model = cp_model.CpModel()
 
diff --git a/examples/python/steel_mill_slab_sat.py b/examples/python/steel_mill_slab_sat.py
index a0f2b43973..bfcb4614d7 100644
--- a/examples/python/steel_mill_slab_sat.py
+++ b/examples/python/steel_mill_slab_sat.py
@@ -158,7 +158,7 @@ class SteelMillSlabSolutionPrinter(cp_model.CpSolverSolutionCallback):
                 print(line)
 
 
-def steel_mill_slab(problem, break_symmetries):
+def steel_mill_slab(problem, break_symmetries) -> None:
     """Solves the Steel Mill Slab Problem."""
     ### Load problem.
     (num_slabs, capacities, num_colors, orders) = build_problem(problem)
diff --git a/examples/python/sudoku_sat.py b/examples/python/sudoku_sat.py
index a6d5fb7f12..664b36bba3 100755
--- a/examples/python/sudoku_sat.py
+++ b/examples/python/sudoku_sat.py
@@ -17,7 +17,7 @@
 from ortools.sat.python import cp_model
 
 
-def solve_sudoku():
+def solve_sudoku() -> None:
     """Solves the sudoku problem with the CP-SAT solver."""
     # Create the model.
     model = cp_model.CpModel()
diff --git a/examples/python/task_allocation_sat.py b/examples/python/task_allocation_sat.py
index f75d190674..8026a71c1d 100644
--- a/examples/python/task_allocation_sat.py
+++ b/examples/python/task_allocation_sat.py
@@ -23,7 +23,7 @@ from absl import app
 from ortools.sat.python import cp_model
 
 
-def task_allocation_sat():
+def task_allocation_sat() -> None:
     """Solves the task allocation problem."""
     # Availability matrix.
     available = [
diff --git a/examples/python/tasks_and_workers_assignment_sat.py b/examples/python/tasks_and_workers_assignment_sat.py
index 0a3631c470..2675bb1a4f 100644
--- a/examples/python/tasks_and_workers_assignment_sat.py
+++ b/examples/python/tasks_and_workers_assignment_sat.py
@@ -34,7 +34,7 @@ class ObjectivePrinter(cp_model.CpSolverSolutionCallback):
         self.__solution_count += 1
 
 
-def tasks_and_workers_assignment_sat():
+def tasks_and_workers_assignment_sat() -> None:
     """solve the assignment problem."""
     model = cp_model.CpModel()
 
diff --git a/examples/python/vendor_scheduling_sat.py b/examples/python/vendor_scheduling_sat.py
index f8c9912373..6f7c9b377a 100644
--- a/examples/python/vendor_scheduling_sat.py
+++ b/examples/python/vendor_scheduling_sat.py
@@ -63,7 +63,7 @@ class SolutionPrinter(cp_model.CpSolverSolutionCallback):
         return self.__solution_count
 
 
-def vendor_scheduling_sat():
+def vendor_scheduling_sat() -> None:
     """Create the shift scheduling model and solve it."""
     # Create the model.
     model = cp_model.CpModel()
diff --git a/examples/python/wedding_optimal_chart_sat.py b/examples/python/wedding_optimal_chart_sat.py
index f86471a78b..df7419154c 100644
--- a/examples/python/wedding_optimal_chart_sat.py
+++ b/examples/python/wedding_optimal_chart_sat.py
@@ -130,7 +130,7 @@ def build_data():
     return num_tables, table_capacity, min_known_neighbors, connections, names
 
 
-def solve_with_discrete_model():
+def solve_with_discrete_model() -> None:
     """Discrete approach."""
     num_tables, table_capacity, min_known_neighbors, connections, names = build_data()
 
diff --git a/examples/python/weighted_latency_problem_sat.py b/examples/python/weighted_latency_problem_sat.py
index 73758fb32e..3e66b61b6e 100644
--- a/examples/python/weighted_latency_problem_sat.py
+++ b/examples/python/weighted_latency_problem_sat.py
@@ -55,7 +55,7 @@ def build_model():
     return x, y, profits
 
 
-def solve_with_cp_sat(x, y, profits):
+def solve_with_cp_sat(x, y, profits) -> None:
     """Solves the problem with the CP-SAT solver."""
     model = cp_model.CpModel()