Who is lying?

Yep, it's Thursday. James speaks the truth on Thursday, and will lie on Friday = TRUE Jonathan speaks the truth on Friday, which is a lie as he said on Thursday "I will lie" = TRUE Since both statements are TRUE, Therefore answer = Thursday

I see some people saying that both James and Jonathan would say "I will lie tomorrow" on Monday.

Let IWLT stand for "I will lie tomorrow" and IWNLT stand for "I will not lie tomorrow."

Consider the following:

@Lalan Shirsat @Gorakh Prasad

Jonathan lies on Tuesdays in which he will say that he will lie by tomorrow but it isnt true because it is thursday. While James tells the truth every thursdays in which by tomorrow he will lie which is true.

You can do this in two ways: 1. Guess and Check (especially because there are only 4 options) 2. Observation and Deduction Observe that both James and Jonathan lie and tell truths on different days. Therefore, for both of them to say "Tomorrow I will lie", one has to be lying while the other has to be telling the truth. Observe the ends and starts of their lying periods (because "Tomorrow") and realise that Thursday will be the day one person is going to stop lying while the other stop saying the truth. Thus Thursday is the right answer

James can say "tomorrow i will lie"on Thursday as its given that he is honest on Thursdays(and on Monday Tuesday Wednesday) and he is giving correct statement because "tomorrow" in his statement means Friday and he lies on Friday(as given) John can say "tomorrow i will lie" on Thursday as its given that he lies on Thursdays(and on Tuesday Wednesday) and he is giving false statement because "tomorrow" in his statement means Friday and he does not lies on Friday(as given)

James can lie on Sunday "I will lie tomorrow", since on Monday he says truth only; James can truly say "I say lie tomorrow" since on Friday on wards he says lie only Johnathan Lies on Thursday" tomorrow i will tell lie" since Friday onwards he says truth only; again he can truly say the same thing on Monday, since he start saying lie from Tuesday on wards. So the common day must be Thursday. A very interesting intelligent question indeed :)

In saying that he will lie "tomorrow," James must be referring to a Friday, Saturday, or Sunday if he is speaking truthfully, because those are his lying days. Otherwise, he is lying, so it must already be Friday or Saturday or Sunday. Jonathan, on the other hand, in saying that he will lie "tomorrow," has to be speaking on a true day if he is referring to Tuesday or Wednesday or Thursday. Otherwise, he is speaking on a lie day and cannot be referring to Sunday or Monday or Tuesday or Wednesday, when he is truthful. The only day on which one man can be lying while the other is telling the truth about the following day is Thursday. Hence, James says truthfully on Thursday that he will lie the following day (Friday), while Jonathan lies on Thursday that he will tell a lie on Friday (which is not one of his lying days).

If it's a day James is lying and tomorrow they will tell the truth, he will lie and say he will lie tomorrow. If he is honest today but not tomorrow... well... it's pretty obvious. But if he is honest both today and tomorrow or dishonest both today and tomorrow he will tell us he will tell the truth tomorrow. Jonathan is the same.

James:Saturday and Friday-dishonest both today and tomorrow, this will not work Monday, Tuesday and Wednesday-honest both today and tomorrow 😞 Sunday and Thursday, however, will work. With Jonathan, he will only say 'Tomorrow I will lie' on Monday and Thursday. Thursday is the answer

The idea is that one of them must be lying about saying "tomorrow i will lie" and because James lies on Thursday's and Jonathan tells the truth on thursday but lies on Friday's, it's given that James is lying

The answer is Thursday.. As we know after reading the question, James has to be honest on Thursday and lie on Friday whereas Jonathan has to lie on Thursday but has to be honest on Friday. So both can say ' Tomorrow I Will Lie ' on Thursday.

James lies on Fridays, Saturdays, and sundays. So on thursday James will say "tomorrow I will lie"=Truth where a Jonathan lies on Tuesdays, Wednesdays, and Thursdays. So on thursday, Jonathan will say " tomorrow I will lie "=LIE. So, yep thursday is correct.

The answer is Thursday since James is saying the truth on Thursday about lying on Friday, And Jonathan is saying a lie on Thursday about lying tomorrow, because if he were saying the truth, he wouldn't be lying on Friday.

James lying days are:

Mon , Tue , Wed , Thu , Fri , Sat , Sun

He can only say "Tomorrow, I will lie" , without causing any contradictions, on Thursday or Sunday:

Thu: should tell the truth $\rightarrow$ "TIWL" $\rightarrow$ lies on Fri $\rightarrow$ told the truth $\Rightarrow$ TRUE

Sun: should tell a lie $\rightarrow$ "TIWL" $\rightarrow$ doesn't lie on Mon $\rightarrow$ told a lie $\Rightarrow$ TRUE $$ Jonathans lying days are:

Mon , Tue , Wed , Thu , Fri , Sat , Sun

He can only say "Tomorrow, I will lie" , without causing any contradictions, on Monday or Thursday:

Mon: should tell the truth $\rightarrow$ "TIWL" $\rightarrow$ lies on Tue $\rightarrow$ told the truth $\Rightarrow$ TRUE

Thu: should tell a lie $\rightarrow$ "TIWL" $\rightarrow$ doesn't lie on Fri $\rightarrow$ told a lie $\Rightarrow$ TRUE

("TIWL" = "Tomorrow, I will lie")

James tell the truth on 2,3,4,5 (fact). So if James says " I will lie tomorrow" on 2,3,4, he must lie on 3,4,5 (contradict with the fact) -> on 2,3,4 disregard. Jonathan tell the truth on 6,7,8 ( interpret similar in James's case) -> 6,7 disregard. Only 5,8 left. Finally got 5 correct.

Well, Thursday is the right answer. According to the given problem, James and Jonathon lie on Specific days, that's Friday, Saturday and Sunday and Jonathon, lies on Tuesday, Wednesday and Thursday. If James says that tomorrrow he would lie, it means that james is speaking the truth as he doesn't lie on Thurday but he does on Friday but for Jonathon, there's Thursday and he lies and definitely he is lying.

Thus, Thursday Is right answer.

It is thursday as , Jonathan lies on thursday,so he's lying and james is honest on thursdays ,so he will speak truth.Therefore both will say so on thursday