Mystery Master	Analysis of Dog Duty	Member

This five-star logic puzzle has 5 noun types, 6 nouns per type, 3 links, 52 facts, and 4 rules. There are several reasons why this puzzle is so difficult:

1. Two dogs are walked two at a time (morning, afternoon, and evening). There could be up to 8 solutions where only the two walks are swapped.
2. The sex for two of the dogs needs to be worked out. Fortunately, it's not very difficult to determine the missing information.
3. One owner has two dogs (one male and one female) walked at the same time. This will be explained in a moment.

Finding Beggare

Scanning the clues for the sex of each dog, we have: the Dalmation and Topal are both males (clue 2), the poodle is female and Beggare is male (clue 3), Dave owns a male dog (clue 4), the bulldog is female (clue 7), the cocker spaniel is male (clue 10). So looking at each breed, we have the following:

1. Bulldog - female
2. Cocker Spaniel - male
3. Dalmation - male
4. Doberman pinscher - unknown
5. German Shepherd - unknown
6. Poodle - female

Clue 1 states that of the three walks, only one has a male and female dog, and these two dogs belong to the same owner. That means the other two walks must have two dogs of the same sex. So we can have either (a) 1 male and 5 females, (b) 3 males and 3 females, or (c) 5 males and 1 female. Since we already have 2 males and 2 females, only (b) can be true. So we are looking for a missing male and a missing female.

If we combine clues (3) Beggare is male, (10) Beggare is not the cocker spaniel (male) or the Dalmatian (male), and (13) Beggare is not the Doberman pinscher (unknown), Beggare must be a male German Shepherd. Which means the Doberman pinscher is female. So now the sex for each dog is known.

1. Bulldog - female
2. Cocker Spaniel - male
3. Dalmation - male
4. Doberman pinscher -female
5. German Shepherd - male
6. Poodle - female

It's pretty obvious now looking at clue 2, which states that Topol is male, but is not the Dalmatian, that Topol must be the male Cocker Spaniel. Though tempting, we'll let the program work that one out.

Because I know the sex of each breed, the nouns for each breed will also tell you the sex of the dog. So I eliminated the noun type for the dog's sex.

Same Owner

Since one owner has two dogs, we need the generic names SameFirst and SameLast, which are paired together. I've added facts that force SameFirst/SameLast to be in the second slot for each walk. When this ends up in a time period with another first name and last name respectively, this will tell us who owns two dogs. Looking at the clues, let's see who cannot own two dogs.

• Clue 1 - the only two dogs walked together of the opposite sex are owned by the same owner. So two dogs of the same sex walked together cannot have the same owner.
• Clue 4 - Dave only owns one dog, a male (clue 4). This means his dog is not walked with SameFirst's dog. Which means his dog is walked with another male dog.
• Clue 8 - John's dog and Ms. Ziel's dogs are walked at the same time (but not after school), so each owns one dog. Because of clues 1 and 4, their dogs must be female.

Walking the Dogs

This puzzle is difficult because there are two dogs that are walked at a time. To avoid duplicates, rule 1 sorts the first names in a walk by their number. This cuts the number of duplicate solutions from 8 down to 2. Furthermore, this rule will also sort the names of the dogs by their number when two dogs are in a walk with SameFirst. This gives us just one solution.

Here are the rules for this puzzle. Note that the first rule restricts the number of duplicate solutions; the other rules are necessary because one person owns two dogs.

1. To avoid duplicates the first names for each walk are sorted by their number (intro).
2. Only the same owner has one male dog walked with a female dog (clue 1).
3. Marie does not own the poodle (clue 3) or the Dalmatian (clue 9).
4. Whiley belongs to a woman (clue 11).

Because we discovered on our own the sex of each breed, the program can find the solution without making any assumptions.

This is one of the most difficult puzzles you will encounter. Like training a show dog, perseverance will lead to a rewarding outcome.