BrainTeaser LogicalAndReasoning NSA Difficult

Problem - 4708

$\textbf{Heist}$

The chief detective hurries down to the police station after hearing big news: there is a heist at Pi National Bank! The police has brought in seven known gang members seen leaving the crime scene. They belong to the nefarious True/False Gang, so named because each member is required to either always tell the truth or always lie. Although everyone is capable of engaging in wrongdoing, the chief also knows from his past cases that any crime committed by this gang always includes one truth teller. When the chief shows up, he asks the gang members the following questions:

1. Are you guilty?
2. How many of the seven of you are guilty?
3. How many of the seven of you tell the truth?

Here are their responses:

• Person $1$: Yes; $1$; $1$
• Person $2$: Yes; $3$; $3$
• Person $3$: No; $2$; $2$
• Person $4$: No; $4$; $1$
• Person $5$: No; $3$; $3$
• Person $6$: No; $3$; $3$
• Person $7$: Yes; $2$; $2$

After looking these answers over, the chief correctly arrests those responsible gang members. Who out of these seven are arrested?

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