```python
# List of possible dates
dates = [
('May', 15), ('May', 16), ('May', 19),
('June', 17), ('June', 18),
('July', 14), ('July', 16),
('August', 14), ('August', 15), ('August', 17)
]
def solve_cheryls_birthday(dates):
# Initial possible dates
possible_dates = dates.copy()
# Step 1: Albert's statement
# Create a count of each day
day_counts = {}
for month, day in dates:
day_counts[day] = day_counts.get(day, 0) + 1
# Filter out months where a unique day exists (Albert knows Bernard doesn't know)
possible_months = set()
for month in set(month for month, day in dates):
month_days = [day for m, day in dates if m == month]
if not any(day_counts[day] == 1 for day in month_days):
possible_months.add(month)
possible_dates = [ (month, day) for (month, day) in possible_dates if month in possible_months ]
# Step 2: Bernard's statement
# Recount the days in the filtered possible dates
day_counts_in_possible = {}
for month, day in possible_dates:
day_counts_in_possible[day] = day_counts_in_possible.get(day, 0) + 1
# Bernard can now deduce the date; keep dates where the day is unique
possible_dates = [ (month, day) for (month, day) in possible_dates if day_counts_in_possible[day] == 1 ]
# Step 3: Albert's final statement
# Recount the months in the possible dates
month_counts_in_possible = {}
for month, day in possible_dates:
month_counts_in_possible[month] = month_counts_in_possible.get(month, 0) + 1
# Albert now knows the date; keep dates where the month is unique
possible_dates = [ (month, day) for (month, day) in possible_dates if month_counts_in_possible[month] == 1 ]
# The remaining date is Cheryl's birthday
if len(possible_dates) == 1:
return possible_dates[0]
else:
return None
# Solve the problem
birthday = solve_cheryls_birthday(dates)
if birthday:
print(f"Cheryl's birthday is on {birthday[0]} {birthday[1]}")
else:
print("Unable to determine Cheryl's birthday.")
```
Cheryl's birthday is on July 16