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.
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
First, let's list out the clues we have:
Clue a: Paula was born in March but not on Saturday.
Clue b: Abigail's birthday was not on Friday or Wednesday.
To solve this puzzle, we can use the process of elimination. Let's go step by step:
Step 1: Determine which sister's birthday is in March.
According to clue a, Paula was born in March. Thus, we can conclude that Paula's birthday is in March.
Step 2: Eliminate Saturday as the possible day for Paula's birthday.
According to clue a, Paula's birthday is not on Saturday. Therefore, we can eliminate Saturday as a possible day for Paula's birthday.
Step 3: Determine which sister's birthday is not on Friday or Wednesday.
According to clue b, Abigail's birthday is not on Friday or Wednesday. Therefore, we can conclude that Abigail's birthday is on Sunday, Monday, or Saturday.
Step 4: Determine which sister's birthday can be on Saturday.
Since Saturday is not available for Paula's birthday, the only remaining option for Saturday is Abigail's birthday.
Step 5: Determine which sister's birthday is on Sunday or Monday.
Since Abigail cannot have Sunday or Monday as her birthday, the only options remaining for Sunday or Monday are the other three sisters: Paula, June, and December.
Step 6: Assign the remaining days to the sisters.
We have Sunday and Monday available for Paula, June, and December. Let's assign Sunday to June and Monday to December.
Finally, we can summarize the results:
Paula: March, (not Saturday)
Abigail: (not Friday or Wednesday), Saturday
June: (not Sunday or Monday), Sunday
December: (not Sunday or Monday), Monday
And the remaining sister, who was not mentioned in the clues, is assigned the last available month, which is February. Therefore, the final answer is:
Paula: March, (not Saturday)
Abigail: (not Friday or Wednesday), Saturday
June: February, Sunday
December: (not Sunday or Monday), Monday
The fifth sister: February, (not mentioned in the clues)
Note: Since the day of the week is not mentioned for the fifth sister, we cannot determine it based on the given clues.