def determine_state(n):
    """
        Recursive Rule:
            - any n bellow 1 is cold because the player who go will loose
            - The number n is hot if at least one case (n-1 or n/2) is cold

    """

    # base recursive case
    if n < 1:
        return "cold"
    else:
        state_1 = determine_state(n-1)
        state_2 = determine_state(n/2)
        if state_1 == 'cold' or state_2 == 'cold':
            return "hot"
        else: return "cold"