Who took the lipstick?

During the lunch hour at school, a group of five girls from Miss Bradley home room visited a nearby store. One of the five girls took a lipstick without paying for it. When the girls were questioned by the school principal, they made the following statements in respective order:

1. Reggie: "Neither Eva nor I did it."

2. Jackie: "It was Reggie or Abby."

3. Abby: "Both Reggie and Jackie are lying."

4. Dana: "Abby's statement is not true; one of them is lying and the other is speaking the truth."

5. Eva: "What Dana said is wrong."

When Miss Bradley was consulted, she said, "Three of these girls are always truthful, but everything that two of them say will be a lie." Assuming that Miss Bradley is correct, can you determine who took the lipstick?


Please argue your answer shortly (to avoid a guessing game)

one of them is lying and the other is speaking the truth.
Assuming this from dana's statement refers to jackie and reggie then:
Technically you cant tell, the only one to point the finger is jackie-
It was Reggie or Abby.
If it was reggie then her statement is a lie, the one below is true, the one below that is a lie, the one below that is true, therefore the bottom one is a lie.
If it was abby her statement is a lie, jackies is true, reggies is true, dana's is a lie(because the first two are true and she says one is lying) and the last statement is a lie because what dana said about abbys statement not being true is not wrong.
Either way we have 3 lies and only two truths, and other than jackie nobody gives any clues as to who did it.

A cursory glance tells me it was abby.

Abby and dana cannot be telling the truth because only two can lie. This invalidates their statements (dont wanna get into the details). Therefore the first two girls are truthful and abby is the thief!

I will post the answer on Sunday (if nobody does post a correct one before.) If a correct argument is posted, I will acknowledge it when I have read it.

A cursory glance tells me it was abby.

Abby and dana cannot be telling the truth because only two can lie. This invalidates their statements (dont wanna get into the details). Therefore the first two girls are truthful and abby is the thief!


Correct. (it was quick)

Congatulations:

A bonus:

King's massenger comes to the town and tells the men there that all unfaithtfull women in the town must be killed. All men in the town know all unfaithfull women (with one exception: they do not know if their own wife is faithfull). Every morning the men of the town gather at the square to announce the killing of the unfaithfull wifes. The third day the Mayor announces the killing of his wife.

Edit: Since this is a translation I see I did't really convey the circumstance that at least one woman in the town is unfaithful one. Riddle would be inconclusive if there were none. Sorry for that.

How many unfaithfull women were in the town alltogether. Argue the case please.

Correct. (it was quick)
Perhaps you'd like to look at it again:
"What Dana said is wrong."
that statement is partly true and partly false, because the 1st part of dana's statement:
Abby's statement is not true
is correct, abbys statement is not true, so not all of what dana said is in fact wrong, only the second part, so it doesnt quite work. ;)

How many unfaithfull women were in the town alltogether. Argue the case please.
Either 1(the mayors is the only one mentioned), or its impossible to tell as no other figures are given.

Either 1(the mayors is the only one mentioned), or its impossible to tell as no other figures are given.

Not impossible, but admittedly difficult...(but that's what riddles are for) :)

PS. It's not a word game, solid logic solves it, you'll see...

Perhaps you'd like to look at it again:

that statement is partly true and partly false, because the 1st part of dana's statement:

is correct, abbys statement is not true, so not all of what dana said is in fact wrong, only the second part, so it doesnt quite work. ;)

Dana specifies what is not true (in which way the statement is not correct):
Dana: "Abby's statement is not true; one of them is lying and the other is speaking the truth."

You scrutinise only a part of it.

Therefore

5. Eva: "What Dana said is wrong."

Eva is not telling the truth.

But anyway to discuss the semantics is not the point.

one of them is lying and the other is speaking the truth.
She is referring to the 1st two, but we already established they are telling the truth, therefore one of them cant be lying, therefore part of dana's statement is a lie, and likewise part is true(the 1st part), therefore Eva is also lying as not all of what dana said is wrong, we now have 3 liars when you said there was only 2, thats what im getting at.
But anyway to discuss the semantics is not the point
I was just trying to prove the riddle needs a slight modifcation, at a glance i was at the same conclusion as the captain, but i kept looking and things dont quite fit.

Not impossible, but admittedly difficult...(but that's what riddles are for)
PS. It's not a word game, solid logic solves it, you'll see...
Thing is you ask how many unfaithful women were there, but no figures about how many men, women or wives there are so a number cannot be determined other than the 1 the mayor is going to kill, therefore the only answer is 1, other than that you wouldnt be able to tell.

She is referring to the 1st two, but we already established they are telling the truth, therefore one of them cant be lying, therefore part of dana's statement is a lie, and likewise part is true(the 1st part), therefore Eva is also lying as not all of what dana said is wrong, we now have 3 liars when you said there was only 2, thats what im getting at.

I was just trying to prove the riddle needs a slight modifcation, at a glance i was at the same conclusion as the captain, but i kept looking and things dont quite fit.

OK I got your point;

But then

1. Reggie: "Neither Eva nor I did it." T

2. Jackie: "It was Reggie or Abby." T

3. Abby: "Both Reggie and Jackie are lying." L

4. Dana: "Abby's statement is not true; one of them is lying and the other is speaking the truth." L

5. Eva: "What Dana said is wrong." T (so Dana is a liar - but not the thief)

But I see that I argued the Dana point wrongly.

But I see that I argued the Dana point wrongly.
It just needs a slight modification, i did get the general idea i just felt like pointing out a tiny flaw for fun, sorry to be a pain, by the way your riddles are pretty good.:)

If you killed one woman a day, then wouldn't there have been three unfaithful women in the village?

If you killed one woman a day, then wouldn't there have been three unfaithful women in the village?
Doesnt say only 1 killed per day, but if so your right.

If you killed one woman a day, then wouldn't there have been three unfaithful women in the village?

Good direction of thinking about the problem, but the reasoning of the riddle is only partially concerned with the number of days. But it is a good start.

There are n whores in town and every husband that has a whore for a wife knows about n-1 whores. I assume only the whore's husband can be the one who kills his wife? Otherwise they'd all be easy pickings...?

So..

If there were only one whore then her husband would know it the first day since he didn't know about any others...

If there are two whores then both husbands would know on the second day since the only other whore they knew about wasn't killed the first day... (meaning that the other whores husband obviously knew about another whore)

If there are three whores then all three husbands would come forth on the third day since two other whore-mongers didn't kill their wifes on the second day, following the same logic...

But why only the mayor?... There's something I'm missing here... Blech... Brainstew..

But why only the mayor?... There's something I'm missing here... Blech... Brainstew..


Good answer. The Riddle doestn't tell about other killings, but they are logically necessary...

If none is killed the first day, the cheated husband knows it must be his one (otherwise he would have to know one other woman cheating..and so on)

Good thinking!!

What i dont get is why they didnt all just gather together on the 1st day and work things out, why did they need three days theres nothing that says they cant all meet at once???

What i dont get is why they didnt all just gather together on the 1st day and work things out, why did they need three days theres nothing that says they cant all meet at once???

Well it depends on how many unfaithful wives there are:

if there were 1 unfaithful wife then all men knew which wife it is (except her husband - so the husband realises: I do not know any unfaithful wife so it must be mine and he would kill her)

but

if there are unfaithful wives the same husband knows one and expects her to be killed the first day - but she is not killed so there must be one more: his..so if there were 2 unfaithful wives they would be killed second day and so on.

Why the men do not tell one another it's just the condition of the riddle world
to make the problem out of it. Using logic kan lead to a lot of info even if you have a limited data.

My logic must just be different then, i would have got together with the guys on day one(since it doesnt say they couldnt) and kill them all on day one. The reason i find this riddle complex is there are no limits specified as to how many men can meet at a time, if the killings can continue after the mayors wife etc.

I don't really understand the logic or moreover the information given. I think someone is killed 1 the first day 2 the second... so the 3rd day must be 6 girls

I don't really understand the logic or moreover the information given. I think someone is killed 1 the first day 2 the second... so the 3rd day must be 6 girls

The formal explanation of the puzzle of the unfaithful wives is to be found:


http://www-formal.stanford.edu/jmc/model/node11.html

the puzzle I put here forward is a "light" form variation of this (original) puzzle. All is fully explained there.