Cheryl

from collections import Counter

def birthday(months):
    # eliminate months with a unique day (albert knows that bernard doesn't know the date)
    c = Counter(day for month in months for day in month)
    possible_months = [(i, month) for i, month in enumerate(months) if all(c[day] > 1 for day in month)]

    # if any remaining month has a unique day, return that (bernard now knows the date)
    c = Counter(day for _, month in possible_months for day in month)
    for i, month in possible_months:
        possible_dates = [day for day in month if c[day] == 1]
        if len(possible_dates) == 1:
            return (i, possible_dates[0])