4
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[This is a puzzle I've been working on. It has a unique solution. This one is meant to be one of the easier ones. Comments, thoughts and suggestions are welcome!]

The suspects are Amos, Celia, Emilia, Gale, Jason, Mendy, Shizue, Timika, Vince.

This is what you know from all those training sessions at the police academy:

  1. Guilty people sometimes lie and sometimes don't.
  2. Guilty people will always say their co-conspirators are innocent (if they mention them).
  3. Innocent people tell the truth (when they know it).
  4. Except for when they make up a statement to try to impress you. But they never make up more than one statement.
  5. The smallest conspiracy that is consistent with the statements is the answer.

In the following table, each line represents the statements made by one of the characters. For example: The I in the first line (Amos) under the letter M represents a statement by Amos that Mendy is innocent.

Statements     | A | C | E | G | J | M | S | T | V |
----------------------------------------------------
Amos           | I |   |   |   |   | I |   | I |   |
----------------------------------------------------
Celia          |   | I | I |   |   | I | I |   | G |
----------------------------------------------------
Emilia         |   | I | I | G |   |   |   | I |   |
----------------------------------------------------
Gale           |   |   |   | I | I |   | I | G | G |
----------------------------------------------------
Jason          | G |   | I |   | I |   |   | G |   |
----------------------------------------------------
Mendy          |   | I | I |   |   | I |   | I | I |
----------------------------------------------------
Shizue         | I |   | I |   | G |   | I |   |   |
----------------------------------------------------
Timika         |   |   |   | G |   | I | I | I |   |
----------------------------------------------------
Vince          | I |   | I | G |   | I |   | I | I |
----------------------------------------------------

Who are the murderers?

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  • $\begingroup$ Are we to assume that the conspiracy is highly incompetent, as in, does every innocent person exactly know who is in the conspiracy and who is not? $\endgroup$ – Bass Dec 12 '18 at 6:49
  • $\begingroup$ No. The innocent people have a subset of information about the others. And potentially have wrong information about one other person. $\endgroup$ – Dr Xorile Dec 12 '18 at 15:47
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Gale and Jason are the murderers.

Reason:

Gale and Jason both say two people are guilty. Since innocent people can lie at most once, for each, either they are guilty or at least one of the people they say is guilty, is. The minimum number of murderers would be if only Timika was a murderer, but this is inconsistent with Emilia and Vince saying Timika is innocent and someone else is guilty, when they could only lie once. The next smallest possibility is if one of Amos, Jason, and Timika is guilty and one of Gale, Timika, and Vince is guilty (Timika paired with either Amos or Vince). Checking cases, Gale and Jason is consistent - Celia made up one Guilty statement.

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  • $\begingroup$ Rot13(Nyfb abobql fnlf gurl ner vaabprag, bgure guna gurzfryirf) $\endgroup$ – Jamie Barker Dec 12 '18 at 10:24
  • $\begingroup$ Any thoughts on the difficulty, eg compared with Sudoku? $\endgroup$ – Dr Xorile Dec 12 '18 at 15:45
  • $\begingroup$ I didn't need to use paper to work it out, so I'd say this one was easier than most sudoku. Though it required more of what I would call two-level reasoning (I don't know the proper term, I mean contradictions, if a then b but c etc.) which can be required in sudoku but usually aren't, so maybe a bit more interesting. This would be harder to work out algorithmically-and-manually than sudoku. $\endgroup$ – justforplaylists Dec 12 '18 at 16:29

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