Fix some issues

backend/solver.py

@@ -27,6 +27,7 @@ def solve_puzzle(index, puzzle, expected_solution, sys_content, sat_cnt_content)
     current_solution = None
 
     while attempts < 3:
+        messages.append({"role": "user", "content": "Make sure you stick to the given categories with strictly identical names otherwise there will be a critical error."})
         attempts += 1
         response = client.chat.completions.create(
             model="gemini-2.0-flash",
@@ -148,7 +149,7 @@ def solve_puzzle(index, puzzle, expected_solution, sys_content, sat_cnt_content)
             cnt_cons += 1
             output = satisfied(constraint)
             if "error" in output:
-                problematic_constraints += f"In line {i + 1}, the {cnt_cons}-th constraint: {constraint}. Error: {output}.\n"
+                problematic_constraints += f"Error when checking {cnt_cons}-th constraint: {output}.\n"
                 ok_satisfied = False
                 break
             if output == "unsat":