Logic Problem?

Question

On a certain campus Arts students always lie and Engineering students always tell the truth.
A stranger meets three students and asks the first if she is studying Arts. The first student answers the question, but the stranger doesn’t hear her. The second student then says to the stranger that the first student denied being an Arts student. Then the third student says that the first is really an Arts student.
How many are Arts students? Can you decide which?

Can you also explain your logic.

Answer 1

A student will always, about themselves, claim to be an Engineering student (either telling the truth, or lying as an Arts student). Thus, the second student must be an Engineering student--they cannot be lying, as no one will ever admit to being an Arts student. If the third student is an Engineer, then the the students are Arts, Engineer, Engineer. If the third student is an Arts student, then they are lying, and in fact the first person is an Engineer. Then, the students are Engineer, Engineer, Arts. Thus, we know for certain that there are two Engineering students and one Arts student, but, we can only determine the Arts student is either the first or the third student, but not which one.

Answer 2

There is only one art student, it is impossible to tell whether it is the first or third student.

No matter what the first student would say she is not an art student, since if she is an engineering student she will tell the truth that she is not an art student and if she is an art student she will lie and say she is not an art student.

Since we know the first student said they are not an art student we know the second student told the truth so they are and engineering student.

The third student said the first student is an art student, if this is true we know that they lied when they said they are not an art student which is consistent with being an art student, however if this is not true they have lied and the first student told the truth.

Therefore there is no way of knowing which is an art student and which is an engineering student, but we know of the 1st and third student one is an engineering student and one is an art student. We also know the 2nd student is an engineering student. So 2 engineering and one Art student

Answer 3

1

Answer 4

1st one is art the other two are engineering. I am not sure though! The 2nd and 3rd both say that the first is an art student, so they are either both liars or both telling the truth, or i may be missing something important with the whole "the first student denied being an art student" said by the 2nd! oh well!!

Answer 5

2 art students

Answer 6

The second student is an Engineering Student

Answer 7

i have to say it is hard to answer becuase the first one answerd but we didnt hear the answer but the second and third said the first one is a art student but the engineers never lie so it's hard but i have say two and three are art students becuase they atcully speaked clearly and liturture is a form of art

Answer 8

You can't tell. There are either 1 or 2 arts students.

2nd person results:
1st - Arts
2nd - Arts
3rd - Engineering

3rd person results:
1st - Engineering
2nd - Engineering
3rd - Arts

Answer 9

their all art students

Answer 10

Well some many people in this planet if you like it is your choice if you like the engineering is fine too i like anything i study aviation it sounds different all people they can do anything what they want and you know that as well too enjoy only you enjoy what you like to do