# 7 Prisoners Say

Prisoner 3 says: "Prisoner 5, Prisoner 6 and I are truthful".

Prisoner 6 says: "Prisoner 5 and Prisoner 1 are truthful".

Prisoner 4 says: "Prisoner 7 lies".

Prisoner 1 says: "Prisoner 4 lies, or Prisoner 2 is truthful".

Prisoner 4 says: "I lie, and also Prisoner 1 and Prisoner 5 are truthful".

Prisoner 2 says: "Prisoner 6 lies, or I am truthful".

Who is telling the truth, and who is lying?

• An answer to what question? – Tweakimp May 3 '18 at 19:35
• Can you double check on your riddle that you got the prisoners talkining right? Prisoner 4 is in there twice and 7 is not in there at all. If you used the numpad to put that in, you might have missed the key :) – Tweakimp May 3 '18 at 19:38
• nope i got it from a piece of paper with it written on and its is exactly as on the paper – dane1 May 3 '18 at 20:16
• @Tweakimp yea i dont know but i would guess its who tells the truth and who is lying – dane1 May 3 '18 at 20:18
• There are no issues with this puzzle if we are savvy enough to understand what he intends. Every one of them is either a truthteller (every entire line must always be logically true) or a liar (every entire line must be the opposite of true). If that is understood, the puzzle works fine and is perfectly clear. – kaine May 4 '18 at 17:57

I'm relatively confident in my answer.

Prisoners 1, 2, and 7 tell the truth and prisoners 3 through 6 lie

Reasoning in order of how I used lines to deduce answers:

Line 5

In order for this to work out logically, 4 must lie. If 4 tells the truth, then the entire statement (including "I lie") must be true. Therefore 4 lies. But how does this work with 4 saying "I lie" and not make that a true statement via double-negative? Because "I lie" is part of a larger statement, that 4 lies and prisoners 1 and 5 are both truthful. In order for the entire statement to compute as a lie, either or both of prisoners 1 and 5 must lie. (Known so far: 4 lies)

Line 4

Prisoner 1 says 4 lies or 2 tells the truth. We know from line 5 that 4 lies, so the entire statement computes as truth. Therefore, we know 1 tells the truth. However, we don't know from this whether or not 2 tells the truth. We'll come back to 2 later. (Known so far: 1 tells the truth; 4 lies)

Line 5: The Sequel

Earlier, we reasoned that the statement as a whole has to come out as a lie, and since we know 4 lies (and therefore that that part of the statement is truthful), at least one of prisoners 1 and 5 must lie. Based on line 4, prisoner 1 tells the truth, so for the entire statement to compute as a combined lie, 5 must lie. (Known so far: 1 tells the truth; 4 and 5 lie)

Line 2

Prisoner 6 says that prisoners 1 and 5 are truthful. We know that 1 is truthful, but 5 lies. Therefore, 6 lies. (Known so far: 1 tells the truth; 4, 5, and 6 lie)

Line 1

Prisoner 3 says that prisoners 3 and 5 and 6 tell the truth. We know that 5 and 6 lie. Therefore, the statement is a lie and 3 lies. (Known so far: 1 tells the truth; 3, 4, 5, and 6 lie)

Line 3

Prisoner 4 says 7 lies. Prisoner 4 lies. Therefore, 7 tells the truth. (Known so far: 1 and 7 tell the truth; 3, 4, 5, and 6 lie)

Line 6

Prisoner 2 says 6 lies or they are truthful. This is not denoted as an exclusive "or" and we know that 6 lies. Therefore, prisoner 2 is truthful. (Known: 1, 2, and 7 tell the truth; 3, 4, 5, and 6 lie)

• Thanks for this it makes alot of sense to me when you put it that way. tho the whole prisoner 4 with its "i lie" statemeant and the double negative seams like an error to me. i will pass this along and maybe it will be usefull thanks – dane1 May 3 '18 at 22:49
• No problem! I'm relying on some specific assumptions, though, including that the puzzle uses the strict logical operation senses of the words "and" and "or" for this to work. – Remilia May 3 '18 at 22:53
• How can you be confident of an answer when the question is so unclear? The only conclusion that can safely be drawn is that Prisoners 1, 2, 3, 4 and 6 can speak some English words. – Peregrine Rook May 3 '18 at 23:36
• One of my assumptions is that the overarching question is, which prisoner(s) tell(s) the truth and which lie? I interpreted the title as declaring this a 7-prisoners "so-and-so says" situation, not necessarily a direct question. A lot of assuming going on, but with that premise, things worked out. If there's a language barrier/possible translation error at play, we might be up a particular creek without a paddle. – Remilia May 4 '18 at 0:16
• It might be more clear if you return to line 5 again after line 4 to determine that 5 lies. I solved this puzzle myself before reading your answer and still didn't catch this logic immediately the way it is organized here. – kaine May 4 '18 at 18:03