# The Inducheon Conspiracy (Who is guilty #7)

At the Korean Nation Police Agency (NPA) in Migeun-dong, Seoul, researchers discovered that 73% of the Senior Inspectors (경감, 警監) all came from the small village of Inducheon. At first they thought it was nepotism. But the truth was far stranger. In this village, the elders set puzzles for the children that trained them to solve mysteries. These children became highly successful detectives.

The rules of this game are very simple. The child play a detective who has to solve a murder mystery (with younger children they use a toy robbery). There is a group of people, some innocent, some guilty, and each makes a number of statements.

1. Innocent people generally tell the truth. They might be mistaken in one of their statements. But if they lie twice, they are guilty.
2. Guilty people cannot be trusted in general - they lie and tell the truth at will. But if they make a statement about another guilty person, they will always say that person is innocent.
3. The smallest conspiracy that is consistent with the statements is the answer

The suspects are Bill, Connie, Darron, Gale, Jed, Laurice, Marcos, Shakia, Tracey (the names have been anglicized).

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

Statements     | B | C | D | G | J | L | M | S | T |
----------------------------------------------------
Bill           | I | G |   | I |   |   | I | G | I |
----------------------------------------------------
Connie         | G | I |   |   |   |   |   |   |   |
----------------------------------------------------
Darron         | I |   | I |   |   |   | G |   | G |
----------------------------------------------------
Gale           |   |   |   | I | I | I |   |   |   |
----------------------------------------------------
Jed            | G |   |   | I | I |   | I |   |   |
----------------------------------------------------
Laurice        | G | I |   |   | I | I |   | I |   |
----------------------------------------------------
Marcos         |   | I | G |   | I |   | I |   |   |
----------------------------------------------------
Shakia         |   | I | G | I | I |   |   | I | G |
----------------------------------------------------
Tracey         | I |   | G | G |   |   |   |   | I |
----------------------------------------------------


For example, you might think that Bill and Darron did it and the others are all innocent. But then Tracey has told two lies (Bill and Gale). So Bill and Darron is not the answer...

Who are the murderers? Can you solve the problem that 6-year-olds from Inducheon solve?

I think the guilty are:

Bill, Marcos, and Tracey

Based on the table:

Anyone accusing two people is either guilty, or right about one of their accusations.

This means that the guilty must include:

B or (C and/or S); D or (M and/or T); S or (D and/or T); T or (D and/or G)

We can rule out:

S, because if S is guilty then D and T can't be, so it would be S, M, G but then B would have 2 wrong

Likewise, we can rule out:

D, because if it's D, then it can't be T, so would have to be D and B or D and S, neither of which is possible

Leaving only:

B, M, T

• Any thoughts on the puzzle from a puzzle-making perspective? Enjoyable? Difficult? Dec 13, 2018 at 2:00
• I quite liked this - it took a bit to wrap my head around the logic, which was a fun challenge. It's a nice twist on the usual 'x always lies, y always tells the truth'. Dec 13, 2018 at 4:44