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Question

There are six civil service job openings. Thirteen candidates passed the civil service exam with equally high scores. So the administrators gave them all a second test. This one had only five questions, each with a Yes/No answer.

The test results of the candidates had thirteen different answer sequences. The top six had the same number of correct answers and were all hired.

• No, No, Yes, No, No

• Yes, No, No, Yes, Yes

• Yes, Yes, Yes, No, Yes

What was the correct sequence of answers?

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no, yes, no, yes, no

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Is it "No, Yes, No, Yes, No"?

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The correct answer sequence is No, Yes, No, Yes, No.

Furthermore, the 6 that were hired must have each

scored 3 correct. They could not have scored higher.

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So everyone had different answer orders, and the top 6 were tied. First of all...

There are only 5 ways to get 4/5 right, so since they had different answer orders, they must have had at most 3/5 right.

However, there are only 5+1=6 ways to get 1/5 or 0/5 right, and 7 people outside of the top 6. This means that at least one of these people got 2/5 right, so the top 6 must have had exactly 3/5 right.

So we need to find an answer sequence for which all of the following orders:

NNYNN

YNNYY

YYYNY

have at most two correct answers. Furthermore, I'll pick the answer order for which two out of three will get each question wrong, which would be NYNYN. This gives the first and second candidates a score of 2/5, and the last a score of 1/5, which works.

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This OP did produce a single solution!

This made me think of a twist:

Would we always have one single solution had K Sengupta chose any other triplet of 3 jobless candidates in that interiew?

N,Y,N,Y,N

If not, what is(are) the triplet(s) that would give more than one possible solution in that case?

Remember, the right sequence is fixed in the spoiler above

The jobless candidates have 2 or less right answers

I hope it's ok with K Sengupta that I posted this.

I hope you find it interesting to prove/disprove.

At least, it was for me!

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There are six civil service job openings. Thirteen candidates passed the civil service exam with equally high scores. So the administrators gave them all a second test. This one had only five questions, each with a Yes/No answer.

The test results of the candidates had thirteen different answer sequences. The top six had the same number of correct answers and were all hired.

• No, No, Yes, No, No

• Yes, No, No, Yes, Yes

• Yes, Yes, Yes, No, Yes

What was the correct sequence of answers?

Answer is No, Yes, No, Yes, No.

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The Answer is [Y N Y Y N]

This is because it is the only combination where all three loser answers given, got at least three wrong.

Every other combo of answers would yield one of those three people getting at least three correct.

Since we know that the winners all got three correct, we know all the losers must have gotten at least three wrong.

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oops! I was wrong. I wrote the OP answers incorrectly on my paper

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There are six civil service job openings. Thirteen candidates passed the civil service exam with equally high scores. So the administrators gave them all a second test. This one had only five questions, each with a Yes/No answer.

The test results of the candidates had thirteen different answer sequences. The top six had the same number of correct answers and were all hired.

• No, No, Yes, No, No

• Yes, No, No, Yes, Yes

• Yes, Yes, Yes, No, Yes

What was the correct sequence of answers?

i think i got it: no yes no yes no

edit: sweet

Edited by heryou

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