Four good friends, who love cats, have each named their cat after one of the other friends. Of the clues that follow, only one is true; the others are false. Which friend owns which cat?
a.Candy’s cat is named either Dody or Alice.
b.Betsy’s cat is named Alice.
c.Either the cat named Candy or the cat named Betsy is owned by Dody.
d.Neither the cat named Betsy nor the cat named Candy belongs to Alice.
e.The cat named Dody does not belong to Candy or Betsy
Clues, maybe slightly rearranged so they all read consistently:
C owns A or D
B owns A
D owns B or C
A owns D (not B or C)
C owns A or B; B owns A or C
Assuming the 1st clue is true, and all the others are false, we now have
C owns A or D
B owns C or D (not A)
D owns A (not B or C)
A owns B or C
B or C owns D
So, we see that
A owns B
B owns C
C owns D
D owns A
Thanks Steve!
Let's analyze each statement one by one:
a. Candy’s cat is named either Dody or Alice.
If this statement is true, then Candy's cat can be either Dody or Alice.
b. Betsy’s cat is named Alice.
If this statement is true, then Betsy's cat is named Alice.
c. Either the cat named Candy or the cat named Betsy is owned by Dody.
If this statement is true, then either Candy's cat is owned by Dody or Betsy's cat is owned by Dody.
d. Neither the cat named Betsy nor the cat named Candy belongs to Alice.
If this statement is true, then neither Betsy's cat nor Candy's cat belongs to Alice.
e. The cat named Dody does not belong to Candy or Betsy.
If this statement is true, then Dody's cat does not belong to Candy or Betsy.
Now let's analyze the statements to see which combinations are possible:
1. If statement a is true, then Candy's cat can be named Dody or Alice.
2. If statement b is true, then Betsy's cat is named Alice.
3. If statement c is true, either Candy's cat is owned by Dody or Betsy's cat is owned by Dody.
4. If statement d is true, then neither Betsy's cat nor Candy's cat belongs to Alice.
5. If statement e is true, then Dody's cat does not belong to Candy or Betsy.
Based on these statements, the possible combinations are:
Option 1:
Candy - Dody
Betsy - Alice
Dody - ???
Alice - ???
Option 2:
Candy - Alice
Betsy - Alice
Dody - ???
Alice - ???
Option 3:
Candy - ???
Betsy - Alice
Dody - ???
Alice - ???
Option 4:
Candy - ???
Betsy - Alice
Dody - ???
Alice - ???
We can't determine the exact combination based on the given clues. There is not enough information to solve the puzzle.
To solve this problem, we need to analyze the clues and eliminate the false statements until only one combination is left. Let's go through each clue one by one:
a. Candy’s cat is named either Dody or Alice.
This clue tells us that Candy's cat can be named either Dody or Alice.
b. Betsy’s cat is named Alice.
This clue tells us that Betsy's cat is named Alice.
c. Either the cat named Candy or the cat named Betsy is owned by Dody.
This clue tells us that Dody owns either Candy's cat or Betsy's cat. So Dody cannot own Alice.
d. Neither the cat named Betsy nor the cat named Candy belongs to Alice.
This clue tells us that Alice does not own Betsy's cat or Candy's cat.
e. The cat named Dody does not belong to Candy or Betsy.
This clue tells us that Dody's cat is not owned by Candy or Betsy.
Now let's analyze the clues and eliminate the false statements:
- From clue a, Candy's cat can be named either Dody or Alice.
- From clue b, Betsy's cat is named Alice.
- From clue c, Dody cannot own Alice, so Dody must own Candy's cat.
- From clue d, Alice does not own Betsy's cat or Candy's cat, so Alice must own Dody's cat.
- From clue e, Dody's cat is not owned by Candy or Betsy, so Dody's cat must be owned by Alice.
Based on the clues, we can conclude:
- Candy's cat is named Dody.
- Betsy's cat is named Alice.
- Dody's cat is owned by Alice.
- Alice's cat is owned by Dody.
Therefore, the final arrangement is:
- Candy owns Dody's cat.
- Betsy owns Alice's cat.
- Dody owns Candy's cat.
- Alice owns Dody's cat.