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Curious Candidate Concern (Posted on 2010-02-02) Difficulty: 3 of 5
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.

See The Solution Submitted by K Sengupta    
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Solution computer-assisted solution | Comment 2 of 3 |

The winning candidates could not have answered more than three correctly, as there are only five possible sets of four correct answers (five ways of determining the sole incorrect answer) but there were six different sets of answers among the winnters, as all 13 candidates had different sets of answers, including these six.

Depending on the correct Y/N sequence, the scores of the non-hires whose answer sequences are shown would be as follows:

NNNNN          4  2  1
NNNNY          3  3  2
NNNYN          3  3  0
NNNYY          2  4  1
NNYNN          5  1  2
NNYNY          4  2  3
NNYYN          4  2  1
NNYYY          3  3  2
NYNNN          3  1  2
NYNNY          2  2  3
NYNYN          2  2  1      *
NYNYY          1  3  2
NYYNN          4  0  3
NYYNY          3  1  4
NYYYN          3  1  2
NYYYY          2  2  3
YNNNN          3  3  2
YNNNY          2  4  3
YNNYN          2  4  1
YNNYY          1  5  2
YNYNN          4  2  3
YNYNY          3  3  4
YNYYN          3  3  2
YNYYY          2  4  3
YYNNN          2  2  3
YYNNY          1  3  4
YYNYN          1  3  2
YYNYY          0  4  3
YYYNN          3  1  4
YYYNY          2  2  5
YYYYN          2  2  3
YYYYY          1  3  4

The only set where all the non-hires scored under three is marked with an asterisk: NYNYN, so that is the correct sequence.

ans$(0) = "N": ans$(1) = "Y"
CLS
FOR a = 0 TO 1
FOR b = 0 TO 1
FOR c = 0 TO 1
FOR d = 0 TO 1
FOR e = 0 TO 1
  s1 = ABS((a = 0) + (b = 0) + (c = 1) + (d = 0) + (e = 0))
  s2 = ABS((a = 1) + (b = 0) + (c = 0) + (d = 1) + (e = 1))
  s3 = ABS((a = 1) + (b = 1) + (c = 1) + (d = 0) + (e = 1))
  PRINT ans$(a); ans$(b); ans$(c); ans$(d); ans$(e),
  PRINT s1; s2; s3,
  IF s1 < 3 AND s2 < 3 AND s3 < 3 THEN PRINT "*":  ELSE PRINT
NEXT
NEXT
NEXT
NEXT
NEXT

 


  Posted by Charlie on 2010-02-02 13:37:02
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