# 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? Commented May 3, 2018 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 :) Commented May 3, 2018 at 19:38
• nope i got it from a piece of paper with it written on and its is exactly as on the paper Commented May 3, 2018 at 20:16
• @Tweakimp yea i dont know but i would guess its who tells the truth and who is lying Commented May 3, 2018 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. Commented May 4, 2018 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 Commented May 3, 2018 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. Commented May 3, 2018 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. Commented May 3, 2018 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. Commented May 4, 2018 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. Commented May 4, 2018 at 18:03

The intended solution seems to involve deducing from the following statement that Prisoner 4 lies and that it is not the case that both Prisoner 1 and Prisoner 5 are truthful:

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

But this deduction is not valid. There is nothing stopping me from saying "I lie, and also Santa Claus is not real." If I did, would you deduce that Santa Claus is real?

The problem is that nothing in the wording of the puzzle implies that all the prisoners' statements are all either true or false. This could be fixed by adding the condition that every prisoner either lies (meaning that every sentence they say is false) or is truthful (meaning that every sentence they say is true).