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You are an investigator. You are to investigate The Joker to know on which day he usually goes on a date with Harley Quinn. The Inspector said that The Joker is lying if and only if it's Monday, Tuesday, Thursday, or Friday (hereby, telling the truth on other days). The Inspector is telling the truth.

You: Well... I hear that you always lie on Monday, Tuesday, Thursday, and Friday; other than those days*... you always tell the truth. Is that correct?

The Joker: Nope, that's not true.

You: Oh, interesting...

The Joker: I was lying yesterday. I... uh...

You: Umm... yea?

The Joker: ...

You: Hmm, are you fine?

The Joker: Tomorrow I'll also lie.

You: Hmm... I see... So the day after tomorrow you'll also lie?

The Joker: Yes I will.

You: And I suppose you were lying yesterday?

The Joker: Yep.

You: Well... Apparently, I already know that today is the day you usually go on a date with Dr. Quinn every week. Poor you to find yourself in this prison today.

The Joker: ...

You: Based on your expression, I can tell that it is indeed today. Thanks a lot Mr. Joker.

So, on which day The Joker usually going on a date?

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  • 2
    $\begingroup$ I'm confused by the second-to-last statement spoken by "you". I had read "I already know today is the day..." to mean that the information given previously was enough to let you know that today is the date-day. However, none of the other statements make any reference to which day he goes on a date.. only to which day it currently is. So... is the real puzzle just to determine which day it currently is, and the whole "when is his date" thing is just unrelated flavor? $\endgroup$ – GendoIkari Mar 14 '18 at 18:00
  • $\begingroup$ @Gendolkari, tbh, yes, the real puzzle is just to determine what day is it. I'm putting it on the conversation to make sure there is no double answer. Spoiler: Wait, double answer? Yes, if you know the solution, you may know that "today" is referring to which day. $\endgroup$ – athin Mar 15 '18 at 2:08
  • $\begingroup$ Thanks. I was mostly just confused by thinking at first that the clues leading up to "I already know that today is the day" were enough information to let you learn that "today is the day", as opposed to that being something "you" already knew before the interview. $\endgroup$ – GendoIkari Mar 15 '18 at 3:04
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The Joker usually goes on a date on

Wednesday.

From the first statement, we know that

the day is Monday, Tuesday, Thursday, or Friday because it contradicts known information.

From the second statement, we can conclude that

it is either Monday or Thursday because he was not lying on the day before.

From the fourth statement, we can conclude that

the puzzle is has a trick to it.

This answer leads to a contradiction, because if it were Monday or Thursday as previously assumed, this statement is true.

From that, we can conclude that at some point,

midnight has passed and the day has changed.

The most obvious time for this to happen is

when he hesitates between the second and fourth statements.

Assuming that, then

there is another contradiction in the sixth statement. If the second statement were the first day, then the second day is either Tuesday or Friday. The sixth statement would then be true on a day that he is lying.

Therefore, we can conclude that

The hesitation is a red herring meant to make us think that the date change happens there, that he is telling the truth on the second day, and that the date change actually happens between the first and second statements.

Knowing the above:

Statements 3, 4, and 5 are all the truth. Meaning that the date at that time is after a day that he lies and before two consecutive days that he lies. The only day that fits these criteria is Wednesday.

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  • $\begingroup$ I was thinking the same thing but standing my ground on what you think is a red herring: I proposed a solution while keeping that twist at the most obvious time $\endgroup$ – Keelhaul Mar 14 '18 at 15:33
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The Joker usually goes on a date on

Sunday

At first I was following the same train of thought as @Apep, which is

Noticing the contradiction if there is no change of day mid-interview, and the contradiction if the change of day happens when the Joker hesitates between the second and fourth statements.

But I decided to keep

The hesitation as a change of day

And followed another lead

The fact that the Joker is always lying if and only if it's Monday, Tuesday, Thursday, or Friday doesn't imply he is always telling the truth the other days! He can both lie and tell the truth at its own convenience those days (as long as he says at least one truth in order not to be always lying).

Hence

When the inspector says "other than those days... you always says the truth. Is that correct?", the Joker is actually telling the truth while answering "Nope". So we are on Wednesday, Saturday or Sunday. His next sentence, "I was lying yesterday", is meaningless, as he can both tell the truth or lie.

But then

A day passes, we're either Monday, Thursday or Sunday. Let's consider we're Monday or Thursday. Then the Joker is lying. But since he says "Tomorrow I'll also lie", which is true, then there is another contradiction!

And from here

The only option left is that we're now Sunday, and the Joker can say whatever he wants... And this from the very beginning!

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  • 1
    $\begingroup$ While this is logically correct with the assumptions, I'm afraid to tell you that The Joker is telling the truth on the other days.. (still need a practice to write a non-ambiguous puzzle imho), +1 btw >< $\endgroup$ – athin Mar 15 '18 at 2:22
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Wednesday

because

the first statement that You ask, you say "I heard that you always lied on Monday, Tuesday, Thursday, and Friday; beside... you always says the truth. Is that correct?" and the Joker responds with "Nope, that's not true".

The trick is

this is supposed to lead us to think that this is a "lying" day, because, after all, we know he lies on Mon, Tues, Thur, and Fri. But he's really saying "That's not true" to the statement that "you always [tell] the truth". So we conclude he is in fact telling the truth, and it must be Wednesday, Saturday, or Sunday.

In other words...

that first statement is asking the Joker "Do you always tell the truth?" to which he responds "No". We (and presumably, the Joker as well) know for a fact that he does not, so this means he's telling the truth.

The next step is to simply

find which day satisfies the rest of the Jokers' true statements, and we find that Wednesday is the current day.

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  • 1
    $\begingroup$ Doesn't beside mean, "other than those days"? $\endgroup$ – Sid Mar 14 '18 at 14:54
  • $\begingroup$ In the context of this sentence, I understood it to mean "after all, you always [tell] the truth..." $\endgroup$ – maxathousand Mar 14 '18 at 14:55
  • $\begingroup$ Oh well, what @Sid said is right. I should edit the question to clarify this, sorry. $\endgroup$ – athin Mar 14 '18 at 14:56
  • $\begingroup$ @athin Shoot.. thought I had it. I'll check back later. $\endgroup$ – maxathousand Mar 14 '18 at 14:58
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    $\begingroup$ @athin, I came to this conclusion as well. I would edit the question to remove "always" from "The Joker is always lying if and only if it's Monday, Tuesday, Thursday, or Friday" if this is not your intended answer. The presence of "always" implies that he must lie on those days, but he can lie on the others. If your intention is to state that he always tells the truth on the days he cannot lie, this modification clarifies that. I responded to this answer because I didn't want to put this as a comment on the main question without the ability to block it with 'spoiler'. $\endgroup$ – iDriveSidewayz Mar 14 '18 at 17:20
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The day is

Friday

The statements are clearly not in-keeping with the rules unless the day changes at some point during the conversation. At Joker's first statement, we know that we begin on a lying day, as he claims the rules (that we've agreed to be implicitly true) are false.

He then goes on to claim that he was lying yesterday, narrowing down the possibilities for our first day to Monday or Thursday.

Then he stammers, which seems the natural place for a change in days to cause him troubles, as he has to switch to telling the truth. But that's confirmed by his next statement, which is that he'll lie tomorrow. If he were still talking on either Monday or Tuesday, he'd be telling the truth in that statement, which he can't do on either of those days. So, it's now either Tuesday or Friday.

He then says that he'll lie the day after too, which is the final logical piece of the puzzle. Because it can no longer be Tuesday, as he would've claimed on that same day that he lies on both Wednesday and Thursday. One of these would be a true statement, the other false, but he's currently incapable of telling a truth. The statement makes sense for Friday, as he will be telling the truth on both Saturday and Sunday, which he's lying about now, on Friday.

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