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Dare to guess what day it is?


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In one small town, there is a liar who lies on six days of the week. But on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 3: "I lie on Wednesday and Friday."

What day does the guy tell the truth?

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Don't have time to work this out right now but you need to set it up differently.

You said:

there is a liar who tells a lie on six days of the week

This means that he tells a single lie, so therefore could be telling the truth otherwise. You need to say "there is a man who tells nothing but lies on six days of the week" or some such.

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And the answer is ...

... He speaks the truth on Tuesdays.

The assertions of Day 1 and Day 3 can't both be true.

Else there would be two truth days: Day 1 and Day 3.

So he cannot lie on all four days mentioned: M T W and F.

The truth day is M T W or F.

The assertions of Day 1 and Day 3 also can't both be false.

Else the truth day would be M or T and also would be W or F, making two truth days.

The truth day is Day 1 or Day 3.

The assertion of Day 2 can't be true.

Else there would be two truth days: Day 2 and Day 1 or Day 3.

Negating Day 2's statement, we see that

Day 2 is M, T, W or F.

Day 2 can't be T or W.

Else Day 1 would be M or T, on which days he claims to lie. A paradox.

Day 2 can't be F.

Else Day 1 would be Th on which he claims to lie M T, and Day 3 would be Sat on which he claims to lie W F.

This makes two truth days: Day 1 or Day 3 [Thu or Sat] and M, T, W or F.

Day 2 is M.

The truth day is Sun or T.

The truth day can't be Sun.

Else, on Day 3 he lies about lying on both W and F, creating two truth days: Sun and W or F.

The truth day is T.

Check:

Day 1 [sun] I lie on M T. [a lie - he speaks truth on T] - OK

Day 2 [Mon] It's Th, Sat or Sun. [a lie - it's M] - OK

Day 3 [Tue] I lie on W F. [the truth - he does lie on those days] - OK

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And the answer is ...

The assertions of Day 1 and Day 3 can't both be true.

Else there would be two truth days: Day 1 and Day 3.

So he cannot lie on all four days mentioned: M T W and F.

The truth day is M T W or F.

Day 1 and Day 3 can both be true because on day 3 he says that he lies on Wednesday AND friday which means if he lies on friday the whole statement is a lie.

But yeah i agree with your final answer.

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Day 1 and Day 3 can both be true because on day 3 he says that he lies on Wednesday AND friday which means if he lies on friday the whole statement is a lie.

But yeah i agree with your final answer.

He tells the truth on only one day of the week.

Since Day 1 and Day 3 are different days of the week, he can't speak the truth both days.

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If the days are consecutive (which should have been clarified) then it could be Saturday or Sunday. Give me something actually solveable.

OP says "three successive days"

It's solvable, just stay with it.

Hint: It can't be either Saturday or Sunday.

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If the days are consecutive (which should have been clarified) then it could be Saturday or Sunday. Give me something actually solveable.

I think the question is clear. It says the statements were made on three successive days ... which is the same as saying on three consecutive days.

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It's very possible I'm not thinking this through, but here's what I thought:

If today IS Thursday, and I'm telling the truth today, then I would be telling the truth to say I lie on Monday and Tuesday, and I lie on Wednesday and Friday. Also, if today is Thursday, and it's my day to tell the truth, that would mean that I lie 6 consecutive days in a row but then on the 7th day I tell the truth.

So couldn't Thursday be my day to tell the truth?

***EDIT***

Sorry I missed the part about the statements being made on different but successive days. I'm wrong. :(

Edited by malar
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And the answer is ...
... He speaks the truth on Tuesdays.

The assertions of Day 1 and Day 3 can't both be true.

Else there would be two truth days: Day 1 and Day 3.

So he cannot lie on all four days mentioned: M T W and F.

The truth day is M T W or F.

The assertions of Day 1 and Day 3 also can't both be false.

Else the truth day would be M or T and also would be W or F, making two truth days.

The truth day is Day 1 or Day 3.

The assertion of Day 2 can't be true.

Else there would be two truth days: Day 2 and Day 1 or Day 3.

Negating Day 2's statement, we see that

Day 2 is M, T, W or F.

Day 2 can't be T or W.

Else Day 1 would be M or T, on which days he claims to lie. A paradox.

Day 2 can't be F.

Else Day 1 would be Th on which he claims to lie M T, and Day 3 would be Sat on which he claims to lie W F.

This makes two truth days: Day 1 or Day 3 [Thu or Sat] and M, T, W or F.

Day 2 is M.

The truth day is Sun or T.

The truth day can't be Sun.

Else, on Day 3 he lies about lying on both W and F, creating two truth days: Sun and W or F.

The truth day is T.

Check:

Day 1 [sun] I lie on M T. [a lie - he speaks truth on T] - OK

Day 2 [Mon] It's Th, Sat or Sun. [a lie - it's M] - OK

Day 3 [Tue] I lie on W F. [the truth - he does lie on those days] - OK

That is true, but what if the 3 days are on 3 different weeks. Then, they would all be true. Plus, it clearly states, that he said these things on 3 SUCCESSFUL days. And it isn't the guy telling that, it's the person writing this.

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I am a newbie, but if this guy lies 6 days of the week, and this is from 3 successful days, itsnt it quite possible that all three days are in the six days that he lies? If so, then all three statements are lies and there for it does not matter what is said because they are false, regardless of AND or OR statements.

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And the answer is ...
... He speaks the truth on Tuesdays.

The assertions of Day 1 and Day 3 can't both be true.

Else there would be two truth days: Day 1 and Day 3.

So he cannot lie on all four days mentioned: M T W and F.

The truth day is M T W or F.

The assertions of Day 1 and Day 3 also can't both be false.

Else the truth day would be M or T and also would be W or F, making two truth days.

The truth day is Day 1 or Day 3.

The assertion of Day 2 can't be true.

Else there would be two truth days: Day 2 and Day 1 or Day 3.

Negating Day 2's statement, we see that

Day 2 is M, T, W or F.

Day 2 can't be T or W.

Else Day 1 would be M or T, on which days he claims to lie. A paradox.

Day 2 can't be F.

Else Day 1 would be Th on which he claims to lie M T, and Day 3 would be Sat on which he claims to lie W F.

This makes two truth days: Day 1 or Day 3 [Thu or Sat] and M, T, W or F.

Day 2 is M.

The truth day is Sun or T.

The truth day can't be Sun.

Else, on Day 3 he lies about lying on both W and F, creating two truth days: Sun and W or F.

The truth day is T.

Check:

Day 1 [sun] I lie on M T. [a lie - he speaks truth on T] - OK

Day 2 [Mon] It's Th, Sat or Sun. [a lie - it's M] - OK

Day 3 [Tue] I lie on W F. [the truth - he does lie on those days] - OK

But have you considered which is the first day of the week, as it could be Saturday or Monday?!

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it is very simple forget every thing it is all in the phrase

"In one small town, there is a liar who lies on six days of the week. But on the seventh day he always tells the truth. He made the following statements on three successive days:"

This is the answer

"But on the seventh day he always tells the truth"

The calendar shows

Sunday- Monday- Tuesday- Wednesday- Thursday - Friday - Saturday

1st day 2nd Day 3rd Day 4th Day 5th Day 6th day 7th day

So it’s Saturday

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Anser to "Dare to guess ?"

.. and it has to be Tuesday.

Here is a Breakdown:

1st Stmt: Sunday : Lie

2nd Stmt: Monday : Lie

3rd Stmt: Tuesday: Truth

.. and btw guessing won't help. This is a very good logic problem.

Kudos :rolleyes:

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In one small town, there is a liar who lies on six days of the week. But on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 3: "I lie on Wednesday and Friday."

What day does the guy tell the truth?

-----------------------------------------------------------------------

At first glance Day 1 statement could only be a truth. Because if he was lying he would be saying he tells the truth on both days.

Day 2 would have to be a lie.

Day 3 then negates the possibility of day one being a truth because if day one was truth he would have to be lying here, but by lying here he says he tells the truth on two days which is impossible.

This, my friends, is called a paradox.

Am I right? Anyone else follow my logic?

My head hurts... :huh:

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Day 1: "I lie on Monday and Tuesday."

At first glance Day 1 statement could only be a truth. Because if he was lying he would be saying he tells the truth on both days.

The entire statement would be a lie if he told the truth on either Monday, OR Tuesday, OR both days. So there are a couple of possibilities here:

1) He Lies on Day 1 and Tells the truth on Monday -OR-

2) He Lies on Day 1 and Tells the truth on Tuesday -OR-

3) He Tells the Truth on Day 1, Lies on both Monday and Tuesday, and Day 1 is not Monday or Tuesday

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 2 would have to be a lie.

Yes, which means Day 2 is Monday, Tuesday, Wednesday, or Friday.

Day 3: "I lie on Wednesday and Friday."

Day 3 then negates the possibility of day one being a truth because if day one was truth he would have to be lying here, but by lying here he says he tells the truth on two days which is impossible.

Same rules for Day 1 apply here. The three possibilities for Day 3 (standing on its own as a statement) are:

1) He Lies on Day 3 and Tells the truth on Wednesday -OR-

2) He Lies on Day 3 and Tells the truth on Friday -OR-

3) He Tells the Truth on Day 3, Lies on both Wednesday and Friday, and Day 3 is not Wednesday or Friday

This, my friends, is called a paradox.

Am I right? Anyone else follow my logic?

My head hurts... :huh:

This isn't a paradox, but there is only one solution.

Premise A: Day 1 he lies, and tells the truth on Monday:

Then Day 1 is not Monday, Day 2 is not Monday (or a paradox would form) or Tuesday. Day 3 is not Tuesday, Wednesday, Friday, Sunday, or Monday (since Day 2 is a lie). This forms a paradox because Day 3 would have to be Truth, but could not be Monday. So Premise A is WRONG.

Premise B: Day 1 he lies and tells the truth on Tuesday:

Then Day 1 is not Tuesday, Day 2 is not Tuesday or Wednesday. Day 3 not Wednesday, Thursday, Friday, Sunday or Monday, leaving Tuesday or Saturday. If Day 3 is Tuesday, then it would have to be Truth, which would mean Wednesdays and Fridays are lies, which fits, so Premise B can be CORRECT.

Premise C: Day 1 he tells the truth, he lies on both Monday and Tuesday:

Day 1 can't be Monday or Tuesday because that would be a paradox. Day 2 can't be Tuesday, Wednesday (because it comes after Day 1 which is not Monday or Tuesday). Day 2 also can't be Thursday, Saturday, or Sunday (because the day before was Truth, so Day 2 can't be), leaving Monday or Friday. Day 3 must be a lie, so Truth must be told on either Wednesday or Friday. Since Day 1 is Truth, then Day 1 must be Wednesday or Friday and Day 2 must be Thursday or Saturday, which it can't be. So Premise C is WRONG.

So:

Truth is told only on Tuesdays, and Day 3 is a Tuesday.

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The answser is Tuesday.

Since there is only one day in a week that he tell the truth, he must tell the truth either on Day 1 or on Day 3.

Then the second day cannot be Thursday, Saturday or Sunday.

Then we can try 4 times (for Monday, Tuesday, Wednesday and Friday) and find out that Day 2 is Monday and he tells the truth on Tuesday.

Let's check it.

Day 1(Sunday): false (he tells the truth on Tuesday)

Day 2(Monday): false (today is Monday)

Day 3(Tuesday): true

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He tells the truth on Tuesday.

On day 3, Tuesday, he tell the truth: he does in fact lie on Wed & Fri.

Day 1 (Sun) is a lie - he does not lie on both Mon and Tues.

Day 2 (Mon) is a lie - today is not Thurs, Sat or Sun.

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Since he cannot be telling anything but truth on Day 1 and 3 or the integrity of the problem falls away since he can only be telling the truth of one of hte problems this problem is paradox.

This man is given to be lying 6 out of 7 days so on only one of these three is it even possible for him to be telling the truth. He could be lying on all three of them, however

IF he is lying on Day 1 about being a liar on Monday and Tuesday that means he is telling the truth on Monday and Tuesday which breaks the given problem since two days are then truth days.

IF he is lying on Day 3 about being a liar on Wednesday and Friday that means he is telling the truth on Wednesday and Friday which breaks the given problem since two days are then truth days.

SO

He has to be telling the truth on Day 1 and Day 3 to have the problems given integrity stay in tact as FOUR days to be truth telling days will break the problem. We call this paradox as there isn't a solution.

Before I realized that I worked on it as thus

M F

T F

W F

R X

F F

S X

S X

Case: All three are lies

Meaning on the six consecutive days we have that we are on three in a row where he is lying, most likely.

Case: Day 1 is correct

Assumed true then it cannot be M or T, case 2 works out and case 3 works out meaning it is either M or T for an answer

~(M ^ T)

which means since he is lying it is also

~(R, S, Su)

Also day 3 if he is lying about lying on Wednesday and Friday then conversely he is saying he does not lie on Wednesday and Friday.

if Incorrect it COULD be M or T but does not have to be

Case: Day 3 is correct

Assumed true it cannot be Wednesday or Friday

~(W ^ F)

Case: Day 2 is correct and Sunday

Case: Day 2 is correct and Thursday

Case: Day 2 is correct and Saturday

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Well, many replies already - but here are my 2 cents...

Tuesday, because...

Day 1: "I lie on Monday and Tuesday."

Day 2: "Today, it's Thursday, Saturday, or Sunday."

Day 3: "I lie on Wednesday and Friday."

What day does the guy tell the truth?

Day 1 and Day 3 can't both be Lie-days, because that would make two Truth-days

If Day 1 is a lie, then Day 3 is true - and Day 3 is Monday or Tuesday (because of the Day 1 lie).

If Day 3 is a lie, then Day 1 is true - and Day 1 is Wednesday or Friday (because of the Day 3 lie).

Truth-day is:

D1=We : No, because then Day 2 would be Thursday

D1=Fr : No, because then Day 2 would be Saturday

D3=Mo : No, because then Day 2 would be Sunday

D3=Tu : Yes

Edited by uhre
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very cleaver. the answer is simple. Day 2.

one expects the answer to be a day of the week i.e monday. but if you look closely you realize the the answer to the question is which day, out of the three successive days, he tells the truth. As we know that he lies for 6 days of the week, we know that on day one ( "I lie on Monday and Tuesday.") he is a lying, for he also lies on another 4 days of the week. the same applies for the statement he made on the third day. thus the answer to the question 'What day does the guy tell the truth?' = day two. (although he is not giving us a direct answer, he is nevertheless telling the truth, and not lying)

I hope that answer makes sense.

Edited by methodman
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