# Is it a contradiction, if C is correct?

A) No
B) Yes
C) No
C) Yes, only if this option is correct
D) Exactly two of all options are correct
E) Of course it is, why shouldn't it be? Any reason?
F) Three above options are correct
G) Four above options are correct
H) No correct option is listed
I) I'm sorry?

Hints: Im gonna give all the hints, you can decide how many you want to uncover.

Hint1

a MCQ. Is that right?

Hint2

in an MCQ you read the options and answer the best (as far as I know)

Hint3

Is a question aware of the options? I don't think so, I think we (people, humans..solvers) are aware of the options.

Hint4

What do you think... In a MCQ, are the options aware of one anothers existance? Not to speak about the contents.

Hint5

What is a contradiction? Does it exist per se? Or without any reason?

Hint6

• Which of the Cs? – trolley813 Jul 15 at 8:39
• I) is definitely the correct answer – Earlien Jul 15 at 8:58
• Uhh! I just see this is not too popular... Is it because it is difficult or bad?:D – FIreCase Jul 15 at 18:14
• @FIreCase I'm doubtful there can be an answer that is logically sound. – Earlien Jul 16 at 10:32

Trying to answer this simulates your brain being mashed to a pulp! I'll have a go though...

This is interpreting the double C option as intentional

Okay, Let's-a go!

Let's declutter the statements and remove any nonsensical ones - I is irrelevant:

A) No
B) Yes
C1) No
C2) Yes, only if this option is correct
D) Exactly two of all options are correct
E) Of course it is, why shouldn't it be? Any reason?
F) Three above options are correct
G) Four above options are correct
H) No correct option is listed


C2 says the statement will contradict itself, ONLY IF it's correct. There seems to be a problem, because both C's contradict each other by both saying yes and no, but C2's answer is based on the fact itself if correct, which it always is (stated in the question!), so it's a contradiction!

Well, that was a bit rubbish, because none of the other statements matter - it's like asking this:

Is this a contradiction, if both statements are true?
A) No
B) Yes


So, now I'll assume the opposite:

This is interpreting the double C option as an accident

Now the uncluttered list looks like this:

A) No
B) Yes
C) No
D) Yes, only if this option is correct
E) Exactly two of all options are correct
F) Of course it is, why shouldn't it be? Any reason?
G) Three above options are correct
H) Four above options are correct
I) No correct option is listed


Saying C is correct means the question is giving us a hint - either:

1) Resolve everything else to give yes, because C says no, so this would give a contradiction
2) Find a contradiction elsewhere whilst trying to prevent one


Now, determining whether options are either correct or incorrect should solve the puzzle, so let's introduce some signs - ✓ and ✗

We already know C is correct, so A must also be correct to match it, and B must be incorrect to avoid a contradiction

A) No                                                       ✓
B) Yes                                                      ✗
C) No                                                       ✓
D) Yes, only if this option is correct
E) Exactly two of all options are correct
F) Of course it is, why shouldn't it be? Any reason?
G) Three above options are correct
H) Four above options are correct
I) No correct option is listed


Now let's look at E - it looks like it's correct, because so far, only two options are correct, but making it correct would also make three options correct, which contradicts itself, so E must be incorrect. Also, I must be incorrect as well, because there must be correct options (also it can't be correct even if it was by itself):

A) No                                                       ✓
B) Yes                                                      ✗
C) No                                                       ✓
D) Yes, only if this option is correct
E) Exactly two of all options are correct                   ✗
F) Of course it is, why shouldn't it be? Any reason?
G) Three above options are correct
H) Four above options are correct
I) No correct option is listed                              ✗


F must be incorrect in the same way B is

D must be incorrect, because then the statement "disappears" from it's own if clause

A) No                                                       ✓
B) Yes                                                      ✗
C) No                                                       ✓
D) Yes, only if this option is correct                      ✗
E) Exactly two of all options are correct                   ✗
F) Of course it is, why shouldn't it be? Any reason?        ✗
G) Three above options are correct
H) Four above options are correct
I) No correct option is listed                              ✗


Now let's look at G and H - G must be incorrect, because A and C are the correct options above G. Therefore, H must be incorrect for the same reason

A) No                                                       ✓
B) Yes                                                      ✗
C) No                                                       ✓
D) Yes, only if this option is correct                      ✗
E) Exactly two of all options are correct                   ✗
F) Of course it is, why shouldn't it be? Any reason?        ✗
G) Three above options are correct                          ✗
H) Four above options are correct                           ✗
I) No correct option is listed                              ✗


Now, it looks like the question is solved, as there is no contradiction, so we can go off and have a nice cup of tea. Wahey!

Edited out bit:

HOWEVER, look at statement E - we've set it as incorrect, which means exactly two statements are not correct, but they are - A and C! Therefore, it must be correct, but it contradicts itself if it is correct, so there is a contradiction

Blimey, that was hard... (I do hope this is right!)

• Oliver! That is just amazing. But if you had your tea, take another look on what you wrote. You have concluded that unfortunately E cannot be correct. Well.. then maybe it is incorrect :D – FIreCase Jul 16 at 13:03
• Agh - darn it! I don't think I was thinking straight - I'll edit the answer – Oliver Jul 16 at 14:11

The question asserts the premise that C is true. The question is whether this case is a contradiction.

There are two C's. So without being able to differentiate them apart, we have to assume both are correct, namely:

C) No (there is no contradiction)
C) Yes (there is a contradiction), only if this option is correct

Since the options are at odds with each other and can't both be true, then C must be a contradiction. This would suggest option B is in fact correct, but then the premise that C is correct is itself a contradiction. Given that C is correct, we would have to accpet that the second C is correct but the first isn't. This is also problematic since the second option implies there is only a contradiction if this (second) option is correct. Yet the contradiction derives from the fact that both option C's were correct, not one, so this second option C by itself cannot be correct. In a similar vein, the first option C cannot be correct because there would be a contradiction when this option says there isn't.

Hence there is no logical solution to this problem as far as I can tell.

• Earlien, thank you very much for your valuable contribution! Very interesting! (Since you didn't answer with a letter, obviously what you wrote can't be a correct answer.) I think the first sentence that slips is "So without being able to differentiate them apart, we have to assume both are correct". – FIreCase Jul 16 at 11:08