Answer to Question #95713 in Algebra for Jas

Question

Abigail, Beth, Celia, Dayna, and Eudora bring their dogs to the Little
Red Schoolhouse for Dogs. During the morning break, they find that
each of their pets has the same name as the husband of one of the other
women.
In particular, they notice these facts.
• Abigail's dog is named George.
. Celia's dog is named Jerry.
• Eudora's dog is named Ike.
• Dayna's dog is named Frank.
• Abigail's husband is also named Frank.
• Beth's husband has the same name as George's wife's dog.
• Horace and his wife, Celia, have the best-behaved dog.
Your job is to figure out the names of each woman's husband and each
woman's dog.
In addition, you must explain clearly how you found your answer. If
you think there is more than one possibility, give all solutions, and
explain why there are no more. If you think there is only one solution,
explain why there are no others.

Answer 1

Let's fill the table with all available information:

Now we can instantly fill Beth's husband cell. The only possible choice is Horace, because other names are occupied either by dogs or by husbands.

Now let's find out, who’s husband's name is George. It could not be Beth, due to 6-th condition. It could not be Dayna, because, in this case, according to the 6-th condition, Beth's husband should be Frank and this name have been already taken. So the only possible choice is Eudora. And, by 6-th condition we instantly get Beth's husband name:

The last step is obviouse:

The solution is the only one, for on each step we made the only possible choice.