How to Test Hypotheses with Property-Based Check in Python

def is_property_satisfied(n):
    """
    Demonstrates a mathematically inspired property:
    checks whether n is both a palindrome and divisible by its digit sum.
    """
    s = str(n)
    if s != s[::-1]:
        return False
    digit_sum = sum(int(d) for d in s)
    return digit_sum != 0 and n % digit_sum == 0


def test_hypothesis(limit):
    """
    Tests a hypothesis: among integers in [1, limit],
    all palindromic integers are divisible by their digit sum.
    Returns the first counterexample, or None if the hypothesis holds.
    """
    for i in range(1, limit + 1):
        if is_property_satisfied(i) and i > 10:
            # Pattern breaks for multi-digit numbers; check small range
            return i
    return None


if __name__ == "__main__":
    limit = 200
    result = test_hypothesis(limit)
    print(f"Hypothesis: all palindromes up to {limit} are divisible by their digit sum.")
    if result is None:
        print("Hypothesis holds within this range.")
    else:
        print(f"Hypothesis fails. Counterexample: {result}")