Mystery Master	Analysis of Six Fearsome Heroes	Member

This three-star logic puzzle should have five stars. It has 5 noun types, 6 nouns per type, 6 links, 34 facts, and 5 rules, where all rules include triggers. It has 360 marks, 60 pairs and 10 grids.

The nouns are grouped by Member, Fizzbin, Chess, Fear, and Hero. Since the last two groups refer to a crew member, I appended "-F" and "-H" to the name of the crew member. For example, when a member is matched with "Data-F", that member fears Data. And when a member is matched with "Data-H", that member's hero is Data. In the introduction it states that nobody fears themselves; nor is there self-hero worship. And nobody fears their own hero. So the first 18 facts cover this information.

Getting nitpicky, I can say "Member A fears member B", but "Member A heroes member B" does not sound right. This would work if the groups were Love and Hate. To be consistent, I should probably treat fear as a noun, and say "Member A's fear is member B" and "Member A's hero is member B", or perhaps "The fear of member A is member B" and "The hero of member A is member B". In pseudocode, this means getFearOf(memberA) is memberB, and getHeroOf(memberA) is memberB.

In case it helps down the road, I switched any links that were "lower than" to "higher than", and I swapped the nouns. The links I ended up with are given below. Note that the relationships "is feared by" and "is hero of" are managed by the rules, and are not links.

1. two positions higher at Fizzbin than
2. four positions higher at Fizzbin than
3. three times higher at 3D chess than
4. two positions higher at 3D chess than
5. higher at 3D chess than

Without making assumptions, the program finds 76/360 marks and 1/60 pairs, with all 5 rules being enforced. So this puzzle is going to need some intense Vulcan logic. The remaining four facts are given below.

20. Troi ranks two positions better than Picard at Fizzbin (clue 2).
30. The person who is worst at Fizzbin is higher than Troi at 3D chess (clue 8).
31. The person ranked 3rd at 3D chess is ranked 4 positions higher than Data at Fizzbin (clue 9).
34. The crew member ranked 2nd at Fizzbin is ranked 2 positions higher at 3D chess than Riker (clue 11).

Below are the rules for this puzzle.

1. Troi is feared by the person Geordi fears (clue 3).
2. The one who is best at Fizzbin ranks 3 times higher at 3D chess than Worf's hero (clue 4).
3. Picard's hero fears Geordi (clue 5).
4. Data is the hero of Riker's hero (clue 7).
5. Riker is feared by the person Picard fears and is the hero of Worf's hero (clue 10).

Fear Rules

Clue 3 says "member X fears Troi", so X is not Troi. It also says "Geordi fears member X", so X is not Geordi. Therefore, we have the fact "Geordi cannot fear Troi." From grid 3, Geordi can fear Data, Picard, or Worf. The members who fear Troi are Data, Picard, or Wolf. The candidates match.

Clue 5 says "Picard's hero is member X", so X is not Picard. It also says "member X fears Geordi", so X is not Geordi. Therefore, we have the facts "Picard's hero cannot be Geordi." and "Picard cannot fear Geordi." From grid 4, Picard's hero can be Data, Riker, Troi, or Worf. From grid 3, the ones who fear Geordi are Data, Riker, Troi, or Worf. The candidates match.

Clue 7 says "member X's hero is Data", so X is not Data. It also says "Riker's hero is member X", so X is not Riker. Therefore, we have the fact "Riker's hero cannot be Data." From clue 4, members who hero can be Data are Geordi, Picard, or Troi. Riker's hero can be Geordi, Picard, or Troi. The candidates match.

Clue 10 says "member X fears Riker", so X is not Riker. It also says "Picard fears member X", so X is not Picard. Therefore, we have the fact "Picard cannot fear Riker". From grid 3, those who fear Riker are Data, Troi, or Worf. And the ones Picard may fear are Data, Troi, or Wolf. The candidates match.

Furthermore, it says "member Y's hero is Riker", so Y is not Riker. And it says "Worf's hero is member Y", so Y is not Worf. Therefore, we have the fact "Worf's hero cannot be Riker". From grid 4, those where Riker is the hero are Geordi, Picard, or Troi. And Worf's hero may be Geordi, Picard, or Troi. The candidates match.

The clues referenced by the rules also gave us the following facts.

1. The best at Fizzbin (6F) is ranked 3 or 6 at 3D chess (clue 4).

Worf's Hero

The reworded clue 4 states "The one who is best at Fizzbin ranks 3 times higher at 3D chess than Worf's hero." This means the best at Fizzbin (6F) must be ranked either 3 or 6 at 3D chess. This situation is covered by the facts. This clue also means Worf's hero is ranked either 1 or 2 at 3D chess. But since we don't know Worf's hero, we must use a rule (rule 2) to cover this situation. And the rule must ensure Worf's hero is not the best at Fizzbin.

From grid 4, Worf's hero can be Geordi, Picard, or Troi, which we'll call memberX. From clue 4, 6F ranks 3 times higher at 3D chess than memberX, so memberX is ranked 1C or 2C. So anyone who cannot be 1C or 2C cannot be memberX. This means Data is not memberX.

From clue 10, the hero of memberX is Riker. From grid 4, memberX can be Geordi, Picard, or Troi. These are the same candidates for Worf's hero. Picard can fear Data, Troi, or Wolf, which we'll call memberY. MemberY must fear Riker, so from grid 3, memberY can be Data, Troi, or Wolf. So far so good.

This puzzle requires rules that can trigger marks to help minimize the number of assumptions. If the program solves this puzzle using assumptions, it needs 11 assumptions to find a solution, and 24 assumptions to exhaust all possibilities. And that's with some very clever rules and triggers. In summary, this puzzle will transport your brain to another galaxy.