Using a matrix, how can we find the names of each woman's husband and dog?

Question

Abigail, Bertha, Candy, Dodi, and Eudora showed up with their puppies at the Little Red Schoolhouse for Dogs. During the morning break, they found that each of their pets had the same name as the husband of one of the women.

Abigail's Dog: George

Candy's Dog: Jerry

Eurdora's Dog: Ike

Abigail's husband: Frank

Bertha's husband shares the same name as George's dog

Horace and his wife Candy have the best-behaved dog

Answer 1

Once the missing piece (the given that Dodi's dog is named Frank) was contributed, the problem becomes much easier.

Abigail's dog is named George.

Candy's dog is named Jerry.

Dodi's dog is named Frank.

Eudora's dog is named Ike.

There is only one possibility: Bertha's dog is named Horace. Now all dog moms are identified.

Abigail's husband is Frank.

Candy's husband is Horace.

It is implied that George is not Bertha's husband. So Bertha must be married to either Jerry or Ike.

Dodi must be married to George, Jerry, or Ike.

Eudora must be married to George, Jerry, or Ike. But since her dog's name is Ike, we can narrow the names of Eudora's husband down to either George or Ike.

That means that George's dog must be either Frank or Ike. That would mean that Bertha must be married to either Ike or Frank. But Frank is already narried to Abigail. So Bertha must be married to Ike. That also means Eudora must be married to George.

Since only Jerry is left, he must be married to to Dodi.

☆☆☆☆☆☆☆☆

There is no need for a matrix to solve this problem. Logic tables work just fine.

Answer 2

Let's set up what we know:

wives: dogs: husbands:

Abigail George Frank

Bertha ? ?

Candy = Jerry = ?

Dodi ? ?

Eudora Ike ?

This is what is given. Now let's see if we can fill in any blanks with what they told us.

Horace and his wife Candy have the best-behaved dog. That means that Horace is Candy's husband.

wives: dogs: husbands:

Abigail George Frank

Bertha ? ?

Candy = Jerry = Horace

Dodi ? ?

Eudora Ike ?

Now, we have two husband's names (Frank and Horace), and neither of them match the dog names we know. We have two blanks in the dog names, so we know those two blanks will be Frank and Horace, but we don't know which one goes where yet:

wives: dogs: husbands:

Abigail George Frank

Bertha Frank/Horace ?

Candy = Jerry = Horace

Dodi Frank/Horace ?

Eudora Ike ?

We are also told that Bertha's husband shares the same name as George's dog. We don't know who George is married to, or his dog's name, but George must be married to either Dodi or Eudora (the only blanks we have other than Bertha). So Bertha's husband must share the name of either Dodi or Eudora's dog, so it must be either Ike, Frank, or Horace. But, Bertha's husband can't be Frank, because Frank is married to Abigail, and it can't be Horace, because Horace is married to Candy, so Bertha's husband must be Ike. And if Bertha's husband is Ike, and he shares the name of George's dog, then George's dog must be Ike (since Eudora's dog is Ike, George must be married to Eudora). If Ike is married to Bertha, and George is married to Eugenia, then there's only one blank husband and the only unused dog name is Jerry, so Dodi's husband must be Jerry.

wives: dogs: husbands:

Abigail George Frank

Bertha Frank/Horace Ike

Candy = Jerry = Horace

Dodi Frank/Horace Jerry

Eudora Ike George

So the only unknowns is which dog belong to Bertha and which dog belongs to Dodi. It looks like there are two possible solutions. Either Bertha's dog is Frank, and Dodi's dog is Horace, or Dodi's dog is Frank and Bertha's dog is Horace. I don't believe there is any way to know which is correct, but if anyone else can justify one solution over the other please let me know!