Based on clue a, we know that Paula's birthday is in March. Since her birthday is not on Saturday, we can eliminate Saturday as an option for the other sisters' birthdays.
Based on clue b, Abigail's birthday is not on Friday or Wednesday. This means her birthday could be on Sunday, Monday, or Tuesday.
Now, let's analyze the remaining clues:
c. The sister born in July was not born on Tuesday or Friday.
Since Abigail's birthday cannot be on Friday, Wednesday, or Tuesday, her birthday must be on Sunday or Monday. Since the sister born in July was not born on Friday or Tuesday, her birthday cannot be on Friday or Tuesday. This means her birthday must be on Sunday, Monday, Wednesday, or Saturday.
d. The sister born in December was not born on Sunday or Monday.
Since the sister born in July cannot have her birthday on Sunday or Monday, her birthday must be on Wednesday or Saturday. Since the sister born in December cannot have her birthday on Sunday or Monday, her birthday must be on Wednesday.
So far, we have:
Paula - March, not Saturday
Abigail - [Unknown], not Friday or Wednesday
[Unknown] - July, not Friday or Tuesday
[Unknown] - [Unknown], not Sunday or Monday
[Unknown] - December, not Sunday or Monday
Let's analyze the remaining clues:
e. Amelia was not born in June or on Wednesday.
Since the sister born in July was not born on Wednesday, and Amelia was not born in June or Wednesday, Amelia's birthday must be in July. This means the sister born in July must be named Amelia.
So far:
Paula - March, not Saturday
Abigail - [Unknown], not Friday or Wednesday
Amelia - July, not Friday or Tuesday
[Unknown] - [Unknown], not Sunday or Monday
[Unknown] - December, not Sunday or Monday
f. Because of other commitments, Amelia did not have her birthday on Thursday.
Since Amelia did not have her birthday on Thursday, her birthday must be either Sunday, Monday, or Saturday. However, since Abigail's birthday cannot be on Sunday or Monday, Amelia's birthday must be on Saturday.
So far:
Paula - March, not Saturday
Abigail - [Unknown], not Friday or Wednesday
Amelia - July, Saturday
[Unknown] - [Unknown], not Sunday or Monday
[Unknown] - December, not Sunday or Monday
g. Charlotte's birthday was in June.
Since the sister born in June is named Charlotte, Charlotte must be the June sister.
Final solution:
Paula - March, not Saturday
Abigail - [Unknown], not Friday or Wednesday
Amelia - July, Saturday
Charlotte - June, [Unknown]
[Unknown] - December, not Sunday or Monday
Now, let's analyze the remaining clues:
b. Abigail's birthday was not on Friday or Wednesday.
Since Abigail's birthday cannot be on Friday or Wednesday, the remaining options are Sunday, Monday, or Tuesday. However, since Amelia's birthday is on Saturday, and Abigail's birthday cannot be on Sunday or Monday, Abigail's birthday must be on Tuesday.
Final solution:
Paula - March, not Saturday
Abigail - Tuesday
Amelia - July, Saturday
Charlotte - June, [Unknown]
[Unknown] - December, not Sunday or Monday
The only month remaining is December, so Charlotte's birthday must be in December.
Final solution:
Paula - March, not Saturday
Abigail - Tuesday
Amelia - July, Saturday
Charlotte - June, December
[Unknown] - December, not Sunday or Monday
Since each sister's birthday month must be different, the remaining sister's birthday must be in February.
Final solution:
Paula - March, not Saturday
Abigail - Tuesday
Amelia - July, Saturday
Charlotte - June, December
Eleanor - February
Therefore, each sister's birthday is as follows:
Paula - March, not Saturday
Abigail - Tuesday
Amelia - July, Saturday
Charlotte - June
Eleanor - February
Five sisters have birthdays in different months from each other (February, March, June, July and December), and on different days of the week from each other (Sunday, Monday, Wednesday, Friday and Saturday). Using the clues below, determine the month and day of the week for each sister's birthday.
a.Paula was born in March but not on Saturday.
b. Abigail's birthday was not on Friday or Wednesday.
1 answer