Politician or Mathmatician

[Edit] First, we have to at least assume that Jim knows whether Joe is a politician or a mathematician, otherwise this problem is irresolvable.

If Joe is a mathematician, he would say that he is a mathematician. If Joe is a politician, he would say he is a mathematician.

If Jane hears Joe saying that he is a mathematician, and then reports that Joe claims to be a mathematician, then Jane is a mathematician.

If Jim is a mathematician, and knows that Joe is a politician, then he correctly states that Joe's claim to be a mathematician to be wrong, and that Joe is a politician. However, if Jim is a politician, and knows that Joe is a mathematician, he would have lied about it and said that Joe's claim to be a mathematician is wrong, and that Joe is a politician.

So, either

1) Joe is a politician, Jane is a mathematician, and Jim is a mathematician, or
2) Joe is a mathematician, Jane is a mathematician, and Jim is a politician.

Either way, there are 2 mathematicians present.

If Joe were a mathematician, he would have truthfully said "I am a mathematician" . If he were a politician he would have falsely said "I am a mathematician" . Therefore we know that Jane is telling the truth (Mathematician) as Joe will definitely have said this.

Jim then goes against Jane by telling her she is wrong, meaning that Jim must be lying (Politician) .

Since Jim is lying and he says Joe is a politician, Joe is a mathematician .

Hence there are 2 mathematicians.

I used an uncommon, random method. First I figured out it is impossible to say you are a politician. If you are a mathematician, you would truthfully say “I am a mathematician”. If you are a politician, you would untruthfully say “I am a politician”. That means Joe said “I am a mathematician. Because we know that, we know John is telling the truth, which means he is a mathematician. We do not know if Joe is telling the truth or not, but we know if Joe is a mathematician, then Jim is a politician and vice versa. This is because if Jim is lying, then the question states Joe is telling the truth, and vice versa.

Hopefully this helps, even though it is confusing.

In Logicala, it is impossible to say "I am a politician" since that carries the same logical fallacy as "This sentence is false." Therefore Joe must have said "I am a mathematician". Jane must be a mathematician from her statement. Lastly, since Joe and Jim are saying contradictory statements, they cannot be the same type of person. Thus, Jane and either Joe or Jim are mathematicians, making 2 total mathematicians.

It's impossible for Joe to say that he is politician since that'll form a paradox, if he was telling the truth he wouldn't be a politician since politicians always lie, and if he was a politician he couldn't say it because that would be the truth. Now we know that the only possible statement from Joe is that he is a mathematician, regardless whether he is politician and lies or mathematician and tells the truth. By this we know that Jane's statement is true, since he did claim he is a mathematician, bringing us to 2 scenarios: Jim is the politician, since he lied that Joes is not a mathematician or Joe is a politician and lied that he is a mathematician and Jim is mathematician, either way, there are 2 mathematicians.

You know what they say, right? There has never been a more wretched inferno of lies and villainy than congress. Oh well, if more people were mathematicians, maybe the world would be a better place.

In this situation, three people from Logicala discuss whether or not our charismatic buddy Joe is a mathematician. So, how many politicians, and how many mathematicians, are present in this discussion?

First of all, notice that Joe always claims to be a mathematician. If he's a mathematician, then his job is to deliver the truth, and if he's a politician, his mouth is a cesspool of lies. Therefore, our friend Jane is a mathematician for sure, as she's telling us exactly what she hears from Joe.

How about our elegant friend Jim, with his black tie and suitcase? If Joe is a mathematician, then Jim is a politician, and vice-versa. See, only a mathematician would be brave enough to dispute the irrational claims of politicians, and only a politician would dare question the impartial truth of mathematics.

In either case, there are definitely two mathematicians in this scenario. Jane is definitely a mathematician, and Joe is a mathematician if and only if Jim is not .

You know, just to be safe, I'm going to take Logicala off my vacation plans. I think I'd prefer Costa Rica or something... any suggestions?

Joe says "either a politician or a mathematician " ,hence he is never wrong. Now ,either one from Jane and Jim must be wrong... Hence,2 truths and a lie. So 2 mathematician and a politician.

Joe without a doubt does not say he is a politician because if he really is a politician, he would tell a lie that he is a mathematician; and if he is a mathematician, he would tell the truth which is his true identity, a mathematician. In either case, Joe is certainly saying he is a mathematician.

If Joe says he is a mathematician and Jane says that Joe claims to be a mathematician, then she is telling the truth. Jane must be a mathematician.

Now let's connect Jim's statement with Joe's true identity. In case 1, if Joe is a politician, then Jim is telling the truth and is a mathematician. In case 2, if Joe is a mathematician, then Jim is telling a lie and is certainly a politician. In either case, there is one person who is a politician and the other is a mathematician.

In the end, Jane is certainly a mathematician and either Joe or Jim is a politician and the other is a mathematician and this concludes that there are 2 mathematicians and 1 politician.

Regardless of his profession, Joe will say that he is a mathematician. Jane correctly reports that Joe says he is a mathematician, so Jane is definitely a mathematician. Jim says two things: "That's wrong," which presumably refers to Jane's statement (since he didn't hear Joe's). And then Jim says that Joe is a politician. Since Jane is not wrong in claiming that Joe said he was a mathematician, Jim must be lying. Ergo, there are two mathematicians. Jane and Joe are mathematicians, and Jim is a politician.

Jim is either a politician or a mathematician If Jim is a politician, then he's lying and hence Joe is a mathematician, so Joe whispers the truth to Jane, that he's a mathematician and she's reporting what he actually said to her, so she's also a mathematician. If Jim is a mathematician, then he's telling the truth, so Joe is indeed a politician and hence he lies to Jane, telling her he's a mathematician, but she's reporting what Joe actually whispered to her, so she tells the truth and hence she's a mathematician. In both cases, there are exactly two mathematicians.

No one here can ever say "I am a politician". A mathematician would be lying and a politician would be telling the truth. Therefore the blank must be filled "mathematician" and Jame is always telling the truth. That's one. If Joe is lying then Jim is telling the truth, and if Joe is telling the truth then Jim Is lying. Exactly one of the two males can ever be telling the truth. That's two, and done.

it will be easy if we listed down the clues: 1. a man will never claim that he/she is a politician since if one is a mathematician then he/she will have to tell the truth and claim that he/she is a mathematician, and if he/she is a politician, he/she will have to lie about he/she identity and therefore state that they were indeed a mathematician. 2. if Joe lies about his identity and Jane claims the fake identity that Joe has stated, Jane will not be considered lying since she is just doing what she was told to, tell everyone what Joe had whispered to her. ----------------------------------------------------------------------separation line--------------------------------------------------------------------- the breakthrough in the problem is that according to clue 1 we know that Joe must've told Jane that he is a mathematician and Jane is telling the truth and must be one of the mathematicians and from there on it separate into two situations: situation 1: Joe is indeed a mathematician and is telling the truth and Jane responded accordingly, leaving Jim as the politician since that he stated that Joe is a politician which in this case is false . ------> in this case, there is 2 mathematicians!! situation 2: Joe is a politician that is lying about his identity and Jane responded accordingly, leaving Joe as the second mathematician since that he stated that Joe is a politician which in this case is true ------> in this case, there is 2 mathematicians!! ---------------------------------------------------------------------------solution------------------------------------------------------------------------- you may have noticed already that in both situations there will be 2 mathematicians and is indeed the answer!! and always remember: failing is just another word for growing!! ˙ ͜ʟ˙

For clarification's sake it should be more clear that Jim is saying that what Joe said is wrong, not that what Jane said is wrong.

Either way you'll get the same answer, but it's important to understanding the problem.

Mathematician = 1 and Politician = 0

if Jane tells the truth ---> Jane = 1 Jim = 0 Joe = 1

if Jane tells a lie ---> Jane = 0 Jim = 1 Joe = 1

Joe's statement that he is either a politician or mathematician is a logically true statement based on the problem setup because if either is true, then that makes the statement true. Joe is a mathematician because he told the truth. Jane's statement is also true because Joe did claim that he was a mathematician (it's one of the inputs to the OR statement). This is true, so Jane is a mathematician. Jim said Joe's true statement (established above) is false, this is a lie. So, Jim is a politician.

In simple form:

• Let's say Joe tells the truth. Jane tells the truth. Jim lies. Mathematicians: 2
• Let's say Joe lies. Jane tells the truth (read below). Jim tells the truth. Mathematicians 2 Let's start with figuring out whether Joe claims to be Mathematician or not. If he is, he would tell the truth by stating that he is a Mathematician. If he was a Politician, he would lie and say he was a Mathematician.

Since Joe said he was a Mathematician, Jane is also a Mathematician because she told the truth.

It doesn't matter whether Jim lies or not because there will still be 2 Mathematicians. If Joe lied by saying he was a Mathematician, Jim told the truth by saying he wasn't. If Joe told the truth, Jim lied. One of them has to tell the truth.

We have Joe, Jane, and Jim. And either of them could lying or telling the truth.

Joe will always have to say “I’m a mathematician” because either he is a lying politician or a truthful mathematician. This makes Jane’s statement automatically true, so she is a mathematician.

If Joe is lying, and is a politician, then Jim is right and is a mathematician. If Joe is telling the truth, then Jim is lying. So either Jane and Joe are mathematicians, or Jane and Jim are mathematicians.

In both scenarios there are two mathematicians, thus the answer.

Neither a politician nor mathematician can say "I am a politician", therefore Joe must have said "I am a mathematician". Therefore, Jane must be a mathematician.

If Joe is a mathematician, Jim must be a politition. If Joe is a politician, Jim must be a mathematician. Therefore there must be two mathematicians either way.

Whether Joe is a mathematician or not, he'll claim to be a mathematician. Thus Jane's statement is true, and she's a mathematician.

Joe's statement and Jim's statement are opposite to each other, therefore one is true and the other is false, i.e., one of the two is a mathematician and the other is a politician.

Thus we have two mathematicians.

If Joe were a mathematician he would be truthful and claim to be a mathematician. If he were a politician he would lie and claim to be a mathematician. Either way we know Joe claims to be a mathematician.

Therefore Jane's statement is true. Therefore Jane is a mathematician.

Jim claims Jane's statement is wrong therefore he is a politician. Therefore his second statement "Joe is a politician" is also false so Joe must be a mathematician.

Therefore 2 mathematicians, Joe and Jane.

We know for sure that Jane thinks she is better than Joe ( looking at the face while reading the line ), so that implies that Joe is saying "I am a mathematician" and also that Jane is a "better" mathematician. For Jim, we can easily tell that he is being sarcastic by his subtle smirk in his face , and also by the fact that he is looking away after Jane says her line.

--> There are 2 mathematicians , Joe and Jane.

Joe says he is a mathematician, because if he says he is a politician, than he would be telling the truth as a politician and lying as a mathematician, which can not happen. Jane reports he says he is a mathematician, so Jane is telling the truth. Now either Joe is a mathematician and Jim is a politician, or Joe is a politician and Jim is a mathematician. Both of these turn out to be 2 mathematicians.

We have to tackle this problem by breaking it down case by case.

First, let’s take the scenario A where Joe is a mathematician. 1) Jane claims that Joe is a mathematician, so Jane is telling the truth, thus she is a mathematician. 2) Jim would be lying by saying Joe is a politician.

Hence, the number of mathematicians is 2.

Second, let’s take the scenario B where Joe is a politician. 1) Joe has claimed to be a mathematician, so Jane would also be telling the truth, thus Jane is a mathematician. 2) Jim may correctly state that Joe is a politician, thus he is a mathematician.

So, the number of mathematicians is also 2.