Agnes Emerald

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logic puzzle help....?

Three sisters own three dogs
Over which they're perfect fools
Each dog gets special gourmet food
And a collar made of jewels

The sister named Luella
Doesn't own the Pekingese
Her dog is either Fritz or Shade;
She feeds him veal and cheese

The dog with emerald collar
Is owned by Agnes or Miss Dolly
He eats only caviar
Shade gets steak, or is the collie

Agnes doesn't own the poodle,
Who wears a collar of green jade
Claude the dog wear diamonds
Dolly's dog is not called Shade

Now you know each doggie's breed
Can match the sisters and their pets
Know each special kind of food
And the collar each one gets.
if you could explain how you figured it out that would be very helpful (:

Luella - Poodle -Fritz - Jade - Veal and Cheese
Agnes - Collie - Shade - Emerald- Caviar
Dolly - Pekinese - Claude - Diamond - Steak

Set up a grid like this and eliminate options as you determine facts
Luella - (Poodle, Collie, Peke) -(Claude,Fritz,Shade) -(Emerald, Diamond,Jade)-(V and C, Caviar, Steak)
Agnes -(Poodle, Collie, Peke) -(Claude,Fritz,Shade) -(Emerald, Diamond,Jade)-(V and C, Caviar, Steak)
Dolly - (Poodle, Collie, Peke) -(Claude,Fritz,Shade) -(Emerald, Diamond,Jade)-(V and C, Caviar, Steak)

2nd Verse - Luella doesn't own the Pekinese, her dog is NOT Claude but she does feed him Veal and Cheese. Delete these options from the grid + delete Veal and Cheese from Agnes and Dolly
3rd verse Emerald collar = Agnes or Dolly - therefore NOT Luella - delete this option. Shade gets steak. We know that Luella's dog gets Veal and cheese, therefore as Shade gets steak, shade is not Luella's dog. Deleting this option means that Luella's dog is FRITZ - last remaining option.
4th verse, Agnes not poodle, therefore also not Jade. Claude the dog wears Diamonds - therefore Luella's dog (Fritz) does not wear diamonds and so must wear JADE the only option left as emeralds have been deleted already. Dollys Dog is not Shade and must be CLAUDE as Luella's is Fritz. This makes Agnes' dog SHADE. Claude wears Diamonds- therefore Dolly's dog has a DIAMOND collar and therefore Agnes's dog EMERALDS last option.
Verse 3 again - Emerald collar (agnes) eats CAVIAR, therefore Dolly's eats STEAK
Verse 3. Shade is either the collie or gets steak. BUT we know that Shade (agnes's dog) gets caviar, therefore Shade must be the COLLIE. Agnes has a Collie.
We have already determined that Luella does not have a Pekinese, now we know she does not have a Collie either. Therefore she must have a POODLE. This means by a process of elimination that Dolly has the PEKINESE.

Final solution

Luella - (Poodle) -(Fritz) -(Jade)-(V and C)
Agnes -(Collie) -(Shade) -(Emerald-(Caviar)
Dolly - (Peke) -(Claude,) -(Diamond)-(Steak)

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