### Brain Teasers

# Liars, Liars...?

In the land of Brainopia, there are three races of people: Mikkos, who tell the truth all the time, Kikkos, who always tell lies, and Zikkos, who tell alternate false and true statements, in which the order is not known (i.e. true, false, true or false, true, false). When interviewing three Brainopians, a foreigner received the following statements:

Person 1:

I am a Mikko.

Person 2:

I am a Kikko.

Person 3:

a. They are both lying.

b. I am a Zikko.

Can you help the very confused foreigner determine who is who, assuming each person represents a different race?

Person 1:

I am a Mikko.

Person 2:

I am a Kikko.

Person 3:

a. They are both lying.

b. I am a Zikko.

Can you help the very confused foreigner determine who is who, assuming each person represents a different race?

### Hint

Pay close attention to Person 3's statements.### Answer

Person 1 is a Mikko.Person 2 is a Zikko.

Person 3 is a Kikko.

Thanks for helping!

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## Comments

Woo, hoo. Me first, me first. That was a great teaser, and I am happy to report that I got this one. Good job

I got it too, but it took a bit of work. Very well done!

Feb 24, 2006

This was a fun teaser, and I enjoyed it! Even though I was able to get it without the hint, I do think, however, that the hint should be changed. It seems to me that it is person 2's comment that is the give away, not 3. .

yay! i got it!!!

that was a VERY good teaser!!!

that was a VERY good teaser!!!

At first I thought number thee had to be the alternater, but I figured out that it made no sense that way. I decided to just assume someone else said ther two statments and got it right from there.

HOlY COW that took me like 20 miutes to figure it out it was awsome

i almost got it

It was okay I suppose...

Mar 02, 2006

Thought it was very easy, almost to easy.

Thanks everyone! *is overwhelmed by positive feedback*

what????????

I almost got it!

A good rework of an oldie.

Thanks guys!

i like this one but it was kinda easy

It was okay. How did person 2 be a ZIkko anyway?

Ohhh. now I know. DOn't tell me anything.

STUPID!! STUPID!! STUPID!!

-Hermione

-Hermione

here is the reason 4 all u confused peoples:

If person 2 said he was a kikko, if he in fact WAS a Kikko, then he would be telling the truth, which is against his race. If he were a Mikko, this statement would obviously be false. Therefore he is a Zikko. This means that person 3 is lying about being a Zikko, which means (s)he is a Kikko. That leaves person 1 as being a Mikko.

If person 2 said he was a kikko, if he in fact WAS a Kikko, then he would be telling the truth, which is against his race. If he were a Mikko, this statement would obviously be false. Therefore he is a Zikko. This means that person 3 is lying about being a Zikko, which means (s)he is a Kikko. That leaves person 1 as being a Mikko.

Cute!! I liked it!!

Great teaser! And I got it!

Yeeyah! I got it! Great Teaser!

Well I sure got it and I loved it! Awesome teaser!

And I should point out that I am not a Kikko or Zikko-- want to be sure you have no doubt that what I said is true!

And I should point out that I am not a Kikko or Zikko-- want to be sure you have no doubt that what I said is true!

LOL... Thanks everyone!

Yay!! i got it! Great teaser by the way!

I got it, too! I like that type of puzzle.

Happy Thanksgiving every body!

Happy Thanksgiving every body!

Only valid if stated that there is only one of each race. Doesn't state that. Could have been two Kikkos and one Mikko.....

J-Mac, the statement "assuming each person represents a different race" means that there is only one of each.

It was fun, but maybe a bit too easy!

Yay! Got it!

Great teaser!

Great teaser!

it would be nice to have an explination after the answer for people who couldn't understand it

easy but fun

Fun and easy! Thanks!

That was confusing, but I got it in the end.

THIS TEASER WAS LAME AND DUMB!

-a Kikko

-a Kikko

I'll second that one...

Davidrools, some people might call your comment offensive - not a very perceptive response to an excellent teaser! Trying to hide behind the Kikko label is a thin disguise!

Who is

Mikkokio?

Mikkokio?

Who is

Mikkokio?

Mikkokio?

That was so easy and obvious it was not even fun!

Uh, no, y'all. Person 3 could also be a Zikko. His first statement, that both Persons 1 and 2 are lying, is false if only one of them is lying or if both of them are telling the truth, and in fact, Person 1 is telling the truth, and Person 2 is lying. Which means that Person 3's second statement, if he is a Zikko, must be true. to wit, he is a Zikko, whose first statement is false, and whose second statement is true. If Person 3 is in fact a Kikko, then both of his statements must be false, and this condition is met if he says he is a Zikko. As for Person 2, he is another Zikko; it just so happens that his first and only utterance is a lie instead of the truth. So it seems that the identity of Person 3 cannot actually be determined: he could be either a Kikko, both of whose utterances are false, or a Zikko, the first of whose utterances is false, and the second of whose utterances is true. He could not, however, be a Zikko, the first of whose utterances is true and the second of whose utterances is false, because if the first utterance is true, then Person 2, as a Kikko, a habitual liar, could not identify himself as such, for to do so would be to tell the truth.

Great for the little ones. Very easy for the grownups.

If person 1 is an 'L/T'(In that order), person 2 a 'T' and person 3 an 'L' then person 2 must be a Kikko. Person 3's first statement is a lie-because person 2 is telling the truth.(Subtle but 'they are both lying' is then a lie.) His second statement is a lie, therefore he is not a Zikko. Hence he must be a Mikko since Kikko is taken. Person 1 is lying-He can not be a Mikko or Kikko, hence he is a Zikko.

Person 2 cannot be a Kikko; if he were, he would not say that he were because Kikkos only lie. If he were a Mikko, he would not say that he weren't, because Mikkos can't lie. Therefore person 2 is a Zikko.

Therefore person 3 is lying about being a Zikko, so he must be a Kikko, which leaves person 1 as the Mikko.

Therefore person 3 is lying about being a Zikko, so he must be a Kikko, which leaves person 1 as the Mikko.

Instead of just the answer, the Solution should provide the process:

1. Person 2 is a Zikko; no one else can make such a statement.

2. If person 3 is telling the truth with statement b, he is a Zikko, and his first statement is false. If lying, he is neither Zikko (which was a lie), nor Mikko (they tell the truth), and is a Kikko. Either way, his "a" statement was false, and Person 1 is a Mikko.

3. Person 3 is a Kikko. Each person represents a different race, and we've ruled out the other two.

1. Person 2 is a Zikko; no one else can make such a statement.

2. If person 3 is telling the truth with statement b, he is a Zikko, and his first statement is false. If lying, he is neither Zikko (which was a lie), nor Mikko (they tell the truth), and is a Kikko. Either way, his "a" statement was false, and Person 1 is a Mikko.

3. Person 3 is a Kikko. Each person represents a different race, and we've ruled out the other two.

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