Whodunit?

[bonanova]

The Threedie brothers, Al, Bert, Chuck, Dick and Eddie, lived in a cabin 3 miles up the old mountain trail, and it was known they didn't get along all that well. This morning, Eddie was found dead behind the cabin, and his brothers, the only suspects in the case, were being questioned by Inspector Sherlock. It was known that, of the four, at least 3 were absolute truth-tellers, and none of them ever lied and told the truth in a single day. All four, of course, denied murdering their brother.

The Inspector started by asking each brother what he had done that morning:

1. Al: I was analyzing random groups of 3 numbers, and I found that if the numbers sum to zero then their product is the average of their cubes.
2. Bert: I was analyzing random polygons with 3 sides, and I found that if I trisected all their angles I could make an equilateral triangle.
3. Chuck: I planted a dozen apple trees out in the orchard, and I found a way to make eighteen rows of 3 trees, each row being dead-on straight.
4. Dick: I went out and ran 3 miles in the woods, and I've figured out that one of my 3 (living) brothers is lying.

The Inspector called in these clues to one of his friends at BrainDen, and in 3 shakes of a lamb's tail the case was solved. The sound you hear is your phone ringing. It's your chance to be famous!

[Molly Mae]

  On 1/14/2018 at 6:34 AM, flamebirde said:

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Well, if all of them are telling the truth except for Dick, it must be Dick. Both of his statements could be false, while everyone else has given a truthful statement. Therefore, Dick must be lying, which means he is the only one who could be a liar.

 

Incidentally - "At least" three of the brothers tell the truth 100%. Could this mean that all of them are telling the truth, and Eddie just committed suicide?

 

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I considered this, but since Dick said another was lying, all of them can't be telling the truth.  I take "is lying" to mean "is lying today" and not "is lying right at this moment."  I also considered plays on the word "lying" (as in, lying down), but the correct form would be "laying" and absolute truth-tellers also don't make mistakes.

Edited January 14, 2018 by Molly Mae

[rocdocmac]

  On 1/14/2018 at 3:31 PM, Molly Mae said:

 

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I considered this, but since Dick said another was lying, all of them can't be telling the truth.  I take "is lying" to mean "is lying today" and not "is lying right at this moment."  I also considered plays on the word "lying" (as in, lying down), but the correct form would be "laying" and absolute truth-tellers also don't make mistakes.

The correct grammatical use for placing yourself in a horizontal position is "lying down", not "laying down", which has to have a direct object, i.e. laying something down). Lie down does not require a direct object. "Lieing" is not to tell the truth! Careful with the spelling!

 

Edited January 15, 2018 by rocdocmac
Moved to spoiler

[Molly Mae]

  On 1/15/2018 at 1:37 PM, rocdocmac said:

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I considered this, but since Dick said another was lying, all of them can't be telling the truth.  I take "is lying" to mean "is lying today" and not "is lying right at this moment."  I also considered plays on the word "lying" (as in, lying down), but the correct form would be "laying" and absolute truth-tellers also don't make mistakes.

The correct grammatical use for placing yourself in a horizontal position is "lying down", not "laying down", which has to have a direct object, i.e. laying something down). Lie down does not require a direct object. "Lieing" is not to tell the truth! Careful with the spelling!

 

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For some reason, my spoilers are disappearing.  Is that normal?

Anyway, I don't think this deserves a spoiler.  Lying can refer to placing oneself in a horizontal position, but it is also the act of being untruthful.  Incidentally, I can find no evidence that "lieing" is an English word.

With that in mind, you could say that Dick has a brother who is currently reclining and nobody murdered anybody in this situation.

[flamebirde]

  On 1/14/2018 at 3:31 PM, Molly Mae said:

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I considered this, but since Dick said another was lying, all of them can't be telling the truth.  I take "is lying" to mean "is lying today" and not "is lying right at this moment."  I also considered plays on the word "lying" (as in, lying down), but the correct form would be "laying" and absolute truth-tellers also don't make mistakes.

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That's true. At least one of the brothers must be lying. I think it must be Dick. Since we have solutions/ proofs of all of the other three, Dick's statement must be false by default (the first half doesn't really matter, since the sentence is an "and" which means both parts must be true to evaluate true).

But why say "At least"? Man, that's gonna drive me up a wall.

 

[Molly Mae]

  On 1/16/2018 at 2:21 AM, flamebirde said:

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That's true. At least one of the brothers must be lying. I think it must be Dick. Since we have solutions/ proofs of all of the other three, Dick's statement must be false by default (the first half doesn't really matter, since the sentence is an "and" which means both parts must be true to evaluate true).

But why say "At least"? Man, that's gonna drive me up a wall.

 

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I think if we're getting into the analysis of the logical AND, we could say that any of them are telling falsehoods.  The trees, for example, could have been pear trees instead, so the entire statement would evaluate false.  I doubt that's the intention of the puzzle.

[flamebirde]

  On 1/16/2018 at 3:31 AM, Molly Mae said:

I think if we're getting into the analysis of the logical AND, we could say that any of them are telling falsehoods.  The trees, for example, could have been pear trees instead, so the entire statement would evaluate false.  I doubt that's the intention of the puzzle.

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But if we've proved that Al, Bert, and Chuck are all correct, then it must be Dick, yes?

 

[rocdocmac]

  On 1/15/2018 at 3:35 PM, Molly Mae said:

Anyway, I don't think this deserves a spoiler.  Lying can refer to placing oneself in a horizontal position, but it is also the act of being untruthful.  Incidentally, I can find no evidence that "lieing" is an English word.

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Oops, you're right! Sorry!

 

[bonanova]

  On 1/14/2018 at 3:31 PM, Molly Mae said:

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I take "is lying" to mean "is lying today" and not "is lying right at this moment."

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Clarification: Dick asserts that he had been out running, and that one of his three brothers has just lied.

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Is this what it feels like to be a Mafia moderator?

Inspector just called in and needs a final answer ... Fame awaits the brave.

[bonanova]

  On 1/16/2018 at 8:46 PM, Molly Mae said:

My guess:

 

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1. Al's statement is provable algebraically.

2. Bert's is proven using Morley's trisector theorem

3. I see rocdocmac's drawing and I wonder if some of those three points are actually collinear.
@bonanova Can any 4 points be collinear?  If not, Chuck gets my accusation.  If they can be, I'll accuse Dick.

 

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Yes, there can be a "bonus" row that contains 4 trees.
Here's an adequate proof of the killer:

 

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• Al, Bert, Chuck and Dick are the only suspects.
• All four deny, so at least one liar.
• At least 3 truthers, so exactly one liar.
• Al, Bert, Chuck describe solvable puzzles, so Dick did not conclude any of them to be liars.
• Dick is thus a liar, so his denial is a lie.
• Dickie did it.

 

[bonanova]

  On 1/14/2018 at 6:39 AM, Thalia said:

For Bert, can you draw lines between points of intersection (like the theorem rocdocmac mentioned) or does the triangle have to be formed from the trisecting lines as attached?

 

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@Thalia,

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ONM.

 

[Thalia]

  On 1/22/2018 at 2:14 PM, bonanova said:

@Thalia,

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ONM.

 

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I understand now. I interpreted it as making the triangle from the lines you get from trisecting. I didn't know you could connect the intersecting points. Thanks for clarifying.