def optimize_problem(problem):
    """
    Generates multiple solution approaches to a problem, tests each one,
    scores them, keeps the best, and improves itself based on what worked.

    Args:
        problem (str): Description of the problem to be solved.

    Returns:
        dict: Dictionary containing the best approach and its score.
    """
    import random

    # Generate multiple solution approaches
    solutions = [random.randint(1, 100) for _ in range(10)]

    # Test each solution and score it
    scores = {solution: abs(solution - int(problem)) for solution in solutions}

    # Keep the best approach
    best_solution = max(scores, key=scores.get)

    return {"best_approach": best_solution, "score": scores[best_solution]}