Mystery Master	Analysis of Abbondanza!	Member

This four-star logic puzzle has 4 noun types, 6 nouns per type, 1 link, 38 facts, and 9 rules. It is a difficult puzzle because some of the nouns are not given, so we need rules to find the placeholders. Please examine this puzzle before you continue reading to see if you can uncover the following evidence.

Nouns

The four noun types are: First Name, Last Name, Pasta, and Sauce. Six nouns are given for the first and last names, but only four are given for the pasta and the sauce. So for the pasta, I have placeholders Pasta5 and Pasta6 where their values are one of the four given pasta dishes. And for the sauce, I have placeholders Sauce5 and Sauce6 where their values are one of the four given sauces.

1. The first names are three females: Andrea, Beth, Candice, followed by three males: Doug, Earl, Frank.
2. The last names are: Gronski, Moulin, Tobin, Vasquez, Wasserman, Zapple.
3. The pasta dishes are: fettuccine, linguine, rigatoni, vermicelli, pasta5, pasta6.
4. The sauces are: Alfredo, carbonara, marinara, pesto, sauce5, sauce6.

The introduction states that each person ordered exactly one pasta, and exactly one sauce. Clue 1 tells us that each kind of pasta and each kind of sauce was ordered at least once. So either one pasta dish was ordered three times, or two different pasta dishes were ordered twice. Same goes for the sauces.

Clue 12 states "Andrea and Moulin both ordered linguine.", so Pasta5 is renamed Linguine2. It is still possible that Pasta6 may be linguine as well. Clues 4, 6, 9, 12, 13 play a role in finding out. Therefore, we can have one pasta (linguine) with three orders, or two dishes of pasta with two orders (pasta6 is not linguine).

Clue 8 states "The only two people whose sauce orders were unique at the table are of the same sex." Therefore, Sauce5 and Sauce6 must have different values. So two of the sauces were ordered by one person each of the same sex, and two of the sauces were ordered by two people each, for a total of six orders. This also means one woman and one man ordered the same sauce.

Clue 13 tells us that Wasserman and Zapple (who are of the same sex) ordered the same kind of sauce. So I will reserve one of the first four sauces for Wasserman, and Zapple is assigned to sauce5. I may need to use a rule to assign sauce6 to the 3rd person of the sex that has the two unique sauce orders (clue 8).

Links

There is only one link, the default link "with". So while the relationships in this puzzle are easy, the challenge is to find the missing nouns.

Facts

There are 38 facts we can glean from the clues, where some of them are unnecessary. The facts alone do not come close to solving this puzzle.

I should point out that based on clues 1, 4, 6, I force Frank and Earl to be with either linguine2 or pasta6. I think that was reasonable considering clues 4 and 6 say they had the same pasta as somebody else. The more interesting question is "Did Frank, Earl, and a woman all have the same pasta?"

The clues that cannot be covered by facts are: 1, 3, 4, 6, 8, 10, 11, 13. We need rules because of the placeholders. A good example is clue 3 "No one ordered linguine pesto." Facts cannot cover this clue because we may find that Pasta6 is linguine, or Sauce5 or Sauce6 is pesto.

Rules

One rule is for clue 11 "Vasquez ordered either rigatoni or carbonara, or both." When a mark has 'X' for Vasquez and rigatoni, this rule triggers an 'O' for Vasquez and carbonara. So this rule covers clue 11.

Another rule is for clue 4 "Frank's pasta was the same as at least one other person's, but not the same as Vasquez's." This rule is complicated because of the placeholders. But one obvious situation to look for is that if Valquez had linguine, Frank did not have linguine.

Gender plays a role for clues 6, 8, and 13. Another rule is for clue 13 where Wasserman and Zapple are of the same sex. When the rule sees that these two cannot be female, it removes all of the female names as possible candidates. In other words, Wasserman and Zapple are two of the three men.

Another rule combines clues 10 and 13. Clue 10 tells us that Earl and Frank ordered different sauces. Clue 13 tells us that Wasserman and Zapple ordered the same sauce. This means Earl and Frank cannot both be Wasserman and Zapple (in some order). This is an exclusive-or situation. When this rule finds that Zapple is either Earl or Frank, it concludes that Wasserman cannot be Earl or Frank. Therefore, Wasserman is Doug.

Clue 10 states Earl and Frank ordered (not necessarily respectively) marinara and pesto for their sauce. Earl has linguine2 with sauce6, but clue 3 prohibits linguine pesto, so sauce6 must be marinara. This means Frank had the pesto sauce. A rule takes care of this situation.

If we enable the rules, we find 204/216 marks and 30/36 pairs. The chart reveals all is known for Andrea, Candice, and Earl.

1. Andrea Vasquez ordered linguine carbonara.
2. Beth's last name is Tobin. Her pasta is rigatoni or vermicelli. Her sauce is marinara.
3. Candice Gronski ordered fettuccine alfredo.
4. Doug's last name is Wasserman. His pasta is rigatoni or vermicelli (clue 13). His sauce is pesto.
5. Earl Moulin ordered linguine2 with sauce6, where the value for sauce6 is marinara.
6. Frank Zapple ordered pasta6 with sauce5. Pasta6 must be rigatoni or vermicelli (clue 13). The value for sauce5 is pesto, which is the same as Wasserman (clue 13).

Clue 6 states "Earl ordered the same pasta as at least one woman." Both Earl and Andrea ordered linguine, so this clue is satisfied.

Clue 8 states "The only two people whose sauce orders were unique at the table are of the same sex." We can see that Andrea's carbonara sauce and Candice's Alfredo sauce are the unique sauces. So this clue is satisfied.

Clue 10 states "Earl and Frank ordered (not necessarily respectively) marinara and pesto." Earl ordered marinara and Frank ordered sauce5 whose value is pesto, so this clue is satisfied.

Clue 9 states "There were exactly as many orders of vermicelli as there were of Alfredo sauce." Since the Alfredo sauce is unique, there must be only one order of vermicelli. This means the value for pasta6 cannot be vermicelli.

Clue 4 states "Frank's pasta was the same as at least one other person's, but not the same as Vasquez's." Since the pasta for Vasquez is linguine, the value for pasta6 cannot be linguine.

Clue 13 states: "Wasserman and Zapple (who are of the same sex) ordered the same kind of sauce, one with rigatoni and the other with vermacelli (not necessarily respectively)." Doug Wasserman and Frank Zapple are both men, so this part of the clue is satisfied. They both ordered pesto, so this part of the clue is satisfied.

Combining clues 9 and 13, the value for Frank Zapple's pasta6 must be rigatoni. So Wasserman's pasta must be rigatoni.

This is a challenging puzzle that uses rules to resolve the placeholders. It also introduces you to "Exclusive-Or" logic.