There are six civil service job openings. Allen, Betty, Candice, Denise, Edwin, Francine, Greg, Hannah, Jane, Kyle, Leon, Mitch, Norman are the thirteen candidates who 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. Three of those who were not hired, had their answer sequences as follows:

• No, No, Yes, No, No
• Yes, No, No, Yes, Yes
• Yes, Yes, Yes, No, Yes

Determine the correct sequence of answers.

As there were 13 distinct answer sequences, nobody could have gotten all of the questions correct. There are also only 5 sequences that would allow for the top six (that is, they miss the 1st, 2nd, 3rd, 4th or 5th question while getting the rest correct). That means that the top six only got 3 of the 5 questions correct. Based on this information, we know that the 3 answer sequences that we are given have at MOST 2 correct answers.

From this, we can see that both the 1st and 5th correct answers must have been "No", as either person #2 or person #3 would get two correct values from the 2nd-4th questions. Now, in order for person #1 to only get 2 correct answers, they must mess up on the middle three questions (as they already got the 1st and 5th correct)

So, our final correct answer sequence is:

No, Yes, No, Yes, No

Posted by Justin on 2010-02-02 13:03:43