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I'm on puzzle 1.3 "The Missing Painting" in the book Montague island mysteries

The Missing Painting

An envelope that was pushed under your door during the night contains this piece of paper:

MYSTERY PUZZLE

Instructions for Taylor

During the night, a priceless painting disappeared from the gallery on the first floor of the mansion. At 10 AM, be in the garden in front of the house. After that, you are free to look around the island and talk to other players. If you should happen to find the painting, you must leave it where it is.

Required for a complete solution

Locate the painting and determine who stole it. Keep in mind that a statement by a guilty party may or may not be true.

Statement you are to give to other players

I am an attorney, and I started in the garden. If the painting is at the windmill, then Jessica is guilty.

Over the course of the next day, you interview everyone and compile the following list of statements:

Statements by the Montagues:

  1. Gordon: The seven guests' occupations are: attorney, banker, composer, decorator, entrepreneur, filmmaker, and gerontologist. The thief acted alone.

  2. Nina: The painting was stolen between midnight and 6 A.M. Either the painting is still somewhere Inside the mansion, or the thief hid it at one of four other locations: the boathouse, the cottage, the lighthouse, or the windmill.

Statements by the staff:

  1. Alistair: At 10A.M. the guests started from seven different locations: the boathouse, cottage, garden, lighthouse, mansion, pond, and windmill.

  2. Evelyn: If the entrepreneur is innocent, the painting is no longer in the mansion.

  3. Grant: The painting is not at the location where the gerontologist started.

  4. Lyle: Karen is the decorator.

  5. Molly: At 10 A.M. the entrepreneur, filmmaker, and gerontologist started at the cottage, mansion, and pond, in some order.

  6. Sandy: If Charles is guilty, the painting is not in the cottage.

Statements by the guests:

  1. Beth: I'm a banker, and I started at the windmill. The painting is not there.

  2. Charles: I'm a gerontologist, and I did not start at either the mansion or the pond.

  3. David: The painting is not in the boathouse or the place where I started.

  4. Frank: I'm not the entrepreneur, but I do know where the entrepreneur started, and it was not the mansion.

  5. Jessica: The painting is not hidden where I started, which was neither the mansion nor the pond.

  6. Karen: I started at the lighthouse. The painting is not hidden in either the boathouse, the lighthouse, or the mansion.

  7. Taylor: I am an attorney, and I started in the garden. If the painting is at the windmill, then Jessica is guilty.

Grid


I'm really struggling to understand the part in Taylor's instructions that says

Keep in mind that a statement by a guilty party may or may not be true.

I can't understand how to figure out who's telling the truth and who's not.

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  • $\begingroup$ Would it be possible to put the full puzzle here for those that do not have access to the book? (or maybe that would entail copyright issues?) $\endgroup$
    – a20
    Mar 23, 2022 at 10:26
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    $\begingroup$ There is an image of this puzzle online here: amazon.in/Montague-Island-Mysteries-Other-Puzzles/dp/… $\endgroup$
    – LeppyR64
    Mar 23, 2022 at 12:20
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    $\begingroup$ Are there assumptions on the introductory pages indicating that the Montagues or the staff are to be trusted? $\endgroup$
    – LeppyR64
    Mar 23, 2022 at 12:50
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    $\begingroup$ @LeppyR64 The puzzles clearly state that what the Montagues and the staff say always will be true. The players are the only ones capable of lying. $\endgroup$
    – WoomyRogue
    Mar 25, 2022 at 1:37

1 Answer 1

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This one seems pretty hard at first glance. I'm going to take it at face value that the Montagues themselves are telling the truth, and therefore that there is only one thief / potential liar, and also that the painting is not at the garden or the pond.

You might start by looking for two or more statements that create some kind of contradiction, which would indicate that one of them must be a lie. For example,

Taylor says that if the painting is at the windmill, then Jessica is guilty. But if the painting is at the windmill, then that makes Beth's statement a lie, which would imply there are two guilty parties, which contradicts our assumption that there is only one. So we might deduce that the painting is NOT at the windmill (or that Taylor is the liar). And proceed from there.

Another approach might be to assume the painting is at a certain location, and then figure out which statement(s) would be lies if you were right. For example,

You might start by assuming that the painting is at the boathouse. But then that would mean both David and Karen are lying, which again contradicts our assumption that there's only one liar. So we might conclude that the painting is NOT at the boathouse. Etc.

I think I've found a solution which is entirely consistent with all of the conditions of the puzzle, although I must admit it's a bit unsatisfying and it certainly does not preclude the existence of other solutions:

It seems possible that the painting is at the cottage, and the thief is Grant. All of the guests, as well as the rest of the staff, would be telling the truth. Beth the banker starts at the windmill; Charles the gerontologist starts at the cottage; David the entrepreneur starts at the pond; Frank the filmmaker starts at the mansion; Jessica the composer starts at the boathouse; Karen the decorator starts at the lighthouse; and Taylor the attorney starts at the garden. I suppose this might imply that Charles found the stolen painting at the cottage but didn't say anything? There's a lot about this puzzle that's ambiguous so I'm not sure if that's an unreasonable assumption.

UPDATE

Per the comment from @WoomyRogue, I'm assuming that neither the Montagues nor the staff can lie. This makes the puzzle significantly easier, and I believe I've found the solution. First,

The painting cannot be at the garden or the pond (Alistair). If the painting is at the windmill, then Beth is lying. This also means either Taylor is lying, or Jessica is guilty. Either way we have two guilty parties, which contradicts Gordon. So the painting is not at the windmill.

If the painting is at the cottage, then Charles is innocent (Sandy). But then Charles is telling the truth, so he's a gerontologist who started at the cottage. This would imply Grant is lying, which isn't possible. So the painting is not at the cottage.

The thief:

Therefore the painting must be at either the boathouse, the lighthouse, or the mansion. This means Karen is lying, and is the thief.

The location:

By David's statement, we know that the painting is not in the boathouse. By Evelyn's statement, we know that if the painting was in the mansion then the entrepreneur would be the guilty party. But we also know that Karen is the decorator (Lyle), so the painting is not in the mansion. Therefore the painting is in the lighthouse.

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