"This test" refers to the following set of three questions. In particular, "questions in this test" can count itself.
Concatenate the answers to the three questions in order. For example, if the answers are 0 , 1 , 2 for Questions 1, 2, 3 respectively, then submit 0 1 2 = 1 2 .
This problem is created by Nikolai Beluhov .
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Why can't it be 110?
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There are 2, not 1, questions having answer the same as Q2 (namely Q1 and Q2).
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Hmm. I don't think you should count the question itself. Maybe the problem should be worded to make that more clear.
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@Colin Carmody – "How many questions in this test" quite unambiguously implies all questions in the test, including itself.
Oh I see, I was not counting the question itself
Why can Question 3 only be either 0 or 1 ?
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If the answer to Question 3 is x , then Question 3 states that the answer is x 2 . This means x = x 2 , which is a simple algebra equation with solutions x = 0 , 1 .
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I see. thanks!
it just says what is the square of the answer to this question. where did they sat they are equal?
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@Raghavendra Mananadi – The answer of Q3 is the square of the answer to Q3. Of course the answer to Q3 is equal to the answer to Q3. If the answer to Q3 is x , then its square is x 2 ; Q3 then says that the answer to Q3 is x 2 . But the answer to Q3 is also x , so x = x 2 .
If 2,1,0 is the answer, then from q3: 0*0=0 which is fine, from q1, the answer to q2 and q3 are different than q1 which is the case as 1 and 0 are both different than 2. But if the answer to q2 is 1, then there is one either q1 or q3 with the same answer as q2. Which is not the case... When you write q1 cannot count q1 itself, it also means that q2 cannot count q2 itself! If this is not the case, than you should specify it in the rules somehow.
However, 1, 1, 0 works according to that logic.
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Q1 cannot count itself since Q1's answer is the same as Q1's answer. If Q1 has answer x , then among the three questions in the test, Q1 itself has answer x and thus is not different from x , hence it's not counted among the questions having answer different from Q1 (that is, different from x ).
On the other hand, the opposite logic works for Q2. If Q2 has answer y , then among the three questions in the test, Q2 itself has answer y and is thus counted among the questions having answer the same as Q2 (that is, the answer y ).
It is confusing. Self-referential statements are confusing.
101 also works!!
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Your answer to Question 2 would be wrong then: there is 1, not 0, question having the same answer to Question 2 (namely Question 2 itself).
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GOT IT NOW ;)
Please add that Q2 counts itself in "Assumptions". If you are trying to solve it without that assumption, you get 201, 101 and 110 as right answers. Which I all tried :(
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@Sasha Chabanov – See my reply in another comment:
"How many questions in this test" quite unambiguously implies all questions in the test, including itself.
I stated that "this test" is the three questions given, so "how many questions in this test" means "how many questions among all these three", which means it counts itself.
You stated in your solution that "Question 1 cannot count Question 1 itself as it clearly has the same answer as itself." But for question 2, you don´t use the same logic, as you did count the answer on question 2. For that matter, i found 101 to be correct also.
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@Yan Coelho – Exactly; Q1 cannot count itself, since Q1 always has the same answer as Q1. Q2 must count itself, since Q2 always has the same answer as Q2.
1,0,1 doesn't work; there is one, not zero, question having the same answer as Q2 (namely Q2 itself).
Why not 211?
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Question 2 is thus wrong. There are two questions with answer 1 (namely Q2 and Q3).
How does "Question 1 states that Question 2 and 3 must have different answers from Question 1". It never says they have to all be different
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If Question 1 has an answer 2 , then the only way to get this is if Questions 2-3 have different answers from Question 1 (otherwise there are less question with different answers).
Why can't 201 be an answer?
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There is 1 question having the same answer to Q2 (namely Q2 itself), not 0.
Why isn't 219 correct?
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Question 3 is then wrong; the square of Question 3's answer is 81, not 9.
Why can it not be 101
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Your answer to Question 2 is wrong (there is one, not zero, question having the same answer as Question 2).
Rubbish. Each question has one answer. But question number 2 asks how many questions have the same answer, which is none !! Simple logic tells you that if two or more questions have the same answer, they would be the same question !! The correct answer must be 201 = 21 !!
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There is one question having the same answer as Question 2, namely Question 2 itself. It doesn't say "how many other questions have the same answer"; it says "how many questions in this test have the same answer".
" if two or more questions have the same answer, they would be the same question" - what?
So ... Question 1: How many arms do you have? Question 2: What's the square root of 4?
Would you consider those to be the same question??
Question 2 is ambiguous. It might very well be read as "how many OTHER questions have the same answer as this question". The problem lies in the interpretation of "having the same answer".
If I'm in a room, and I say "how many people in this room have the same name as me", I am obviously not counting myself.
If you read question 2 like that, the answer is either 201, 110, 101, or 211. :)
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I intentionally state "how many questions in this test have the same answer", and I've also said that "this test" refers to the three questions, not the two other questions.
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Hey, we all make mistakes. Just admit that you blew it on this problem, and lets move on. Whats done is done
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@DarkMind S. – No, I don't admit that I blow the problem, because I can likewise say that the people answering Q2 to read "other questions" to fail at reading. (I intentionally phrase the problem to make it unambiguous as possible, with "this test refers to the following three questions".) Nevertheless, I clarified it in the problem that all questions can count themselves. (And now I'll expect people thinking that Q1 counts itself.)
why q3 is either 0 or 1
Hi, What about 121?
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Q2's answer is wrong (only one question has the same answer as Q2).
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By looking on each question individually first, we get the following:
Now, seeing that no other question has an answer of 3 , Question 2 cannot have an answer of 3 as well. If Question 2 has an answer of 2 , then the only other question that can give an answer of 2 is Question 1, but Question 1 states that Question 2 and 3 must have different answers from Question 1, contradiction. Thus Question 2 has an answer of 1 ; this forbids any other question for an answer of 1 , so Question 3 has an answer of 0 . Finally, Question 1 cannot have an answer of 0 as Question 2 has a different answer from it, so Question 1 has an answer of 2 .
This gives the unique solution 2 , 1 , 0 , giving the answer 2 1 0 .