Example solutions via IBM ILOG CPLEX 12.9.

source/MOSS.py

@@ -94,7 +94,7 @@ def solve_board(initial_board, max_solve_time=120000):
             sum(objective_vars[:, j]) == sum(range(board_len+1)))
 
     # Set constraint: nonet sums
-    constraint_nonet = []
+    # constraint_nonet = []
     if board_len == 9:
         solver.Add(
             sum(sum(objective_vars[0:3, 0:3])) == sum(range(0, board_len + 1)))

source/examples.py

@@ -29,9 +29,9 @@
     [0, 1, 0, 2, 0, 0, 4, 0, 0],
     [3, 0, 0, 0, 0, 5, 0, 1, 0]
 ])
-mb9_sol = solve_board(medium_board_9, max_solve_time=10800000)
+mb9_sol = solve_board(medium_board_9, max_solve_time=10800000)  # unfortunately, COIN CBC cannot solve this problem
 print(mb9_sol['solution'])
-with open("mb9.lp", "w") as text_file:
+with open("mb9.lp", "w") as text_file:  # therefore, export to lp, and solve with CPLEX
     print(mb9_sol['lp_file'], file=text_file)
 
 # 9x9 difficult board
@@ -49,4 +49,21 @@
 db9_sol = solve_board(difficult_board_9, max_solve_time=1200000)
 print(db9_sol['solution'])
 with open("./lp_files/db9.lp", "w") as text_file:
-    print(db9_sol['lp_file'], file=text_file)
+    print(db9_sol['lp_file'], file=text_file)
+
+# Evil board
+evil_board_9 = np.array([
+    [1, 0, 6, 0, 0, 7, 0, 0, 3],
+    [9, 2, 0, 0, 3, 0, 0, 0, 0],
+    [0, 5, 0, 0, 8, 0, 0, 6, 0],
+    [0, 0, 0, 8, 0, 0, 0, 0, 6],
+    [0, 1, 0, 0, 0, 0, 0, 5, 0],
+    [5, 0, 0, 0, 0, 4, 0, 0, 0],
+    [0, 8, 0, 0, 9, 0, 0, 2, 0],
+    [0, 0, 0, 0, 2, 0, 0, 9, 4],
+    [6, 0, 0, 3, 0, 0, 7, 0, 8]
+])
+eb9_sol = solve_board(evil_board_9)  # unfortunately, COIN CBC cannot solve this problem
+print(eb9_sol['solution'])
+with open("./lp_files/eb9.lp", "w") as text_file:  # therefore, export to lp, and solve with CPLEX
+    print(eb9_sol['lp_file'], file=text_file)