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Partial solution to “The Pirates of Beal Isle”

This is some workings towards a solution for “The Pirates of Beal Isle”, a logic puzzle at http://puzzling.stackexchange.com/q/11474/4692

I don't claim they're necessarily correct, but they're as far as I got before I gave up. They might be useful to somebody else tackling the puzzle. Think of it as a sort of "hint sheet", if you like :-)

I'm not posting this as an answer because I want the question to remain unanswered until somebody has a complete solution. I want to see it answered, so that I can see what I missed.

Note: my first attempt was based on a misinterpretation of Richard's clue "No sailors on the English ship were maimed"; I thought that meant nobody was killed. A revised attempt is in attempt2.md.

POTENTIAL SPOILERS BEWARE

Since Gist doesn't have spoiler blocks, here are some pictures from Placekittens to pad out the text.

Who are the pirates?

This seems like a natural starting point. If we can find the pirates (or at least, narrow it down), we can regard the other castaways as honest, and use their clues to rat out the pirates.

Some observations:

  • The first pirate is Larry.

    Debra refers to the “only male officer” on one of the ships. Every ship but the Cavadonga has at least two male officers, so this ship must be the Cavadonga. It follows that Liao Jin-Zhong is male.

    Emily is the only Chinese survivor, and there are only two Chinese officers on the manifest: Yan Fu-ju (gender unknown) and Liao Jin-Zhong (male). She must be Yan Fu-ju, the Boatswain of the Cheswick.

    Larry tells us that the Boatswain of the Cheswick has full use of both-hands, but Emily has a hook hand, so he is lying. Larry is a pirate.

  • At least one of Richard and Jack is a pirate.

    They make contradictory statements about the sailors on the Cheswick:

    • Jack says that there was a grave for Virginia Allen, who is listed on the manifest as one of the sailors on the Cheswick.
    • Richard says that none of the sailors on the Cheswick were hurt.

    They cannot both be right.

  • At least one of Edward, Frank and Patrick is lying.

    We can count 13 officers who survived, which means that 7 officers died. Now consider the following clues:

    • Edward: only 1 officer survived aboard the Cheswick (so 3 died).
    • Frank: at least 1 officer died on each ship.
    • Patrick: 2 officers on the English ship survived (so 2 died).

    If all three were correct, then at least 8 officers would be dead. Somebody is lying.

Larry {Richard, Jack} {Edward, Frank, Patrick}

That accounts for at least three of the pirates. We know there are exactly four pirates, which means we have one pirate left to find.

I don’t know who the final pirate is yet, but we have enough to rule out several people:

There are several pairs of people who say the same thing, so we can now regard them as honest. (If one is lying, then so is the other, but then we'd have more than four pirates.) These are:

  • Anthony and Margaret
  • Charles and Rosemary
  • Elizabeth and Ryan
  • Gary and Sherry
  • Irene and Terry
  • Megan and Willie

Combined with the knowledge of the first pirate, and we can start filling in the grid.


Filling in the grid, part 1

Here are some observations based on the people we know are telling the truth:

  • Per Rosemary, each ship is named after the language of its home country, and so the Leeuw must be Dutch.

    Larry claims that the captain of the Dutch ship doesn't wear an eye patch; but he's a pirate, so he's lying. She does have an eye patch.

    Eliminating candidates who don't have an eye patch, we see that the captain of this ship is either Ann, Debra or Kimberly.

  • Ann tells us that she has an American superior officer; it follows that if she is telling the truth, she is not the captain of her ship.

    Suppose she is lying, and she is the captain of the Golden Leeuw. Josephine tells us that the captain of the Leeuw has a hook hand, which Ann does not. So Josephine would also be lying, but that makes five pirates. Contradiction.

    We deduce that Ann is not the captain of the Leeuw.

    Similarly, suppose Ann is lying, and she is the captain of the Cavadonga. Emily tells us that the captain of the Cavadonga is American, which Ann is not (she is Jamaican). Again, we have five liars, so Ann is not captain of the Cavadonga.

  • Elizabeth was a cabin girl, which means she sailed on the Vierge or the Fox. Since Ryan was on her boat, he must also have been on one of these two ships.

  • Terry tells us that there is somebody who shares his first name, and that this person is either English or Australian. All of the stowaways are American, so his namesake must appear on the manifest. The only name which is repeated on the manifest is Samuel. We deduce that Terry is one Samuel, and the other (if he survived) is English or Australian.

    Since Irene is on the same ship as Terry, she must be on one of these two ships.

  • Anthony is travelling with Margaret. There are no positions for female sailors aboard the Cavadonga, so he cannot be aboard this ship.

  • Both Anthony and Margaret talk about a boat going from a French port to an American port. Since there are five ports listed distinctly at each end, Kimberly's reference to the same trip means she's telling the truth.

    Then Kimberly tells us that all the 2nd Mates have eyepatches. So we can rule out Jason as the second mate on the Cheswick.

    We deduce the 2nd mate on the SeaFox and Cheswick both died.

We can cross off quite a few other possibilities by using accent/nationality information:

  • Carrie, Christina and Raymond are the only Spanish survivors, and so they must correspond to the four Spaniards on the manifests (Piperion, Pulqueria, Felipe and Margarita).
  • Keith is the only survivor with a Russian accent, so he must be either Gennadi or Vasya, and the other Russian is dead.
  • Jason is the only survivor with a Dutch accent. There are three Dutch names on the manifest: Henrick, Tjeerd and Ruud. Since Jason is an officer, Ruud (a sailor) has perished. Jason must be one of the other two Dutch officers.
  • Dennis and Kevin are both American, which means we can rule them out of roles which don't have English names (Seigfried, Hartmut, Arno).
  • Emily is the only Chinese survivor, and she is an officer. This means the other two Chinese on the manifest (Hu Wei-Xue and Liao Jin-Zhong) must have died. The latter tells us that Debra is honest.
  • Larry and Richard are German and French/German, respectively. This means we can rule them out of officer roles with English names (Roger, Christopher, Henry).

Another deduction based on grid logic:

  • The remaining possibilities for Josephine are 2nd Mate on the Vierge, or any position on the Cavadonga.

    She tells us that she hired a Jamaican cabin boy, which is impossible on the Vierge (which only has a cabin girl). So if she's 2nd Mate on the Vierge, then she's a pirate. But Kimberly tells us that all 2nd Mates have eye patches, which Josephine does not, so Kimberly would also be a pirate. This gives us at least five pirates; contradiction.

    We deduce that Josephine did not travel on the Vierge.

Who are the pirates?

This seems like a natural starting point. If we can find the pirates (or at least, narrow it down), we can regard the other castaways as honest, and use their clues to rat out the pirates.

Some observations:

  • Larry is a pirate.

    Debra refers to the “only male officer” on one of the ships. Every ship but the Cavadonga has at least two male officers, so this ship must be the Cavadonga. It follows that Liao Jin-Zhong is male.

    Emily is the only Chinese survivor, and there are only two Chinese officers on the manifest: Yan Fu-ju (gender unknown) and Liao Jin-Zhong (male). She must be Yan Fu-ju, the Boatswain of the Cheswick.

    Larry tells us that the Boatswain of the Cheswick has full use of both-hands, but Emily has a hook hand, so he is lying. Larry is a pirate.

  • At least one of Edward, Frank and Patrick is lying.

    We can count 13 officers who survived, which means that 7 officers died. Now consider the following clues:

    • Edward: only 1 officer survived aboard the Cheswick (so 3 died).
    • Frank: at least 1 officer died on each ship.
    • Patrick: 2 officers on the English ship survived (so 2 died).

    If all three were correct, then at least 8 officers would be dead. Somebody is lying.

Filling in the grid, part 1

Already we can start filling in part of the grid:

  • Larry tells us that the boatswain of the Cheswick had full use of both hands. Since he's lying, this boatswain must have hooked hands. This leaves either Emily or Kimberly (if this officer survived).

  • Anthony and Margaret both talk about a ship going from France to America. Only one pair of places could fit this description: Bordeaux to Charleston, which is a journey also described by Kimberly. Since all three describe the same journey, they are either all pirates or all honest. If they were all pirates, then we would have at least five pirates, so they must be all honest.

  • Anthony is on the same ship as Margaret, who is a female sailor. There are no positions for female sailors on the Cavadonga, so Anthony cannot be on this ship.

  • Kimberly tells us that all the 2nd Mates have eye patches. From this, we can conclude:

    • Josephine is not 2nd Mate on the Vierge
    • Neither Dennis nor Kevin is not 2nd Mate on the Sea Fox
    • Jason is not 2nd Mate on the Cheswick, and so this officer perished. Instead, Jason is the captain of the Vierge.

We can also use accent/nationality data to fill in quite a bit more:

  • Carrie, Christina and Raymond are the only Spanish survivors, and so they must correspond to the four Spaniards on the manifests (Piperion, Pulqueria, Felipe and Margarita).

  • Keith is the only survivor with a Russian accent, so he must be either Gennadi or Vasya, and the other Russian is dead.

  • Jason is the only survivor with a Dutch accent. There are three Dutch names on the manifest: Henrick, Tjeerd and Ruud. Since Jason is an officer, Ruud (a sailor) has perished. Jason must be one of the other two Dutch officers.

  • Dennis and Kevin are both American, which means we can rule them out of roles which don't have English names (Seigfried, Hartmut, Arno).

  • Emily is the only Chinese survivor, and she is an officer. This means the other two Chinese on the manifest (Hu Wei-Xue and Liao Jin-Zhong) must have died. The latter tells us that Debra is honest.

  • Larry and Richard are German and French/German, respectively. This means we can rule them out of officer roles with English names (Roger, Christopher, Henry).

Now it gets a little more protracted, and I was getting one grid square at a time:

  • Ann is not the captain on the Leeuw.

    For suppose she is. Then Ann is lying about having an American superior officer, and Josephine is lying about the captain of the Leeuw having a hook-hand; thus the four liars are

    Larry, Edward/Frank/Patrick, Ann, Josephine

    We can now trust everybody else, and prove this leads to more than four pirates.

    Now we know that Jason is captain of the Vierge, Ann of the Leeuw, and either Carrie or Christine on the Sea Fox. Since Jack tells us that two captains died, we deduce that the captains of the Cheswick and Cavadonga both died.

    Rosemary tells us that each ship was named in the language of its home country, so the Vierge is French. Then Anthony tells us that the Vierge is headed for Casa Blanca, and Raymond tells us the Boatswain on this ship was killed.

    We now know where the seven casualties among the officers are:

    • Boatswain on the Vierge
    • Either the Boatswain on the Sea Fox or the 1st Mate on the Cheswick
    • The 2nd Mates on the Sea Fox, the Cheswick and the Cavadonga
    • The Captains of the Cheswick and the Cavadonga

    We may deduce that Frank is lying, as all of the officers on the Leeuw have survived. So the four liars are Larry, Frank, Ann and Josephine.

    Since only one officer survived on the Cheswick (Edward), Keith must be the Boatswain on the Sea Fox.

    Per Rosemary, the English ship is either the Sea Fox or the Cheswick, which suffered 1 and 3 losses among the offices, respectively. This contradicts Patrick's statement that 2 officers on the English ship were killed.

    We deduce that Ann is not captain of the Leeuw.

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commented Apr 14, 2015

One or two more notes:

  • We know there are four pirates, so I was trying to find four disjoint sets, each of which contained at least one pirate. We could then deduce that everybody not in these sets was honest, and use their clues to find the real pirates. But according to the comments, the original party-goers didn’t know how many pirates there were, so it should be solvable without knowing that.

    It’s probably possible to work out everybody’s pirate/not-pirate status directly.

  • tl;dr: I know that Larry is a pirate, one of Richard/Jack is a pirate, and one of Edward/Frank/Patrick is a pirate.

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