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Testing Three Students (Posted on 2013-11-20) Difficulty: 2 of 5
3 students are taking an examination of N subjects.
Points are awarded according to the positions in each subject they took.

The person who gets 1st will get the highest points, followed by 2nd and lastly 3rd. (So let 1st=X points, 2nd=Y points, 3rd=Z points.)

Student B obtained X points in English.
Student A obtained 22 points total.
Students B and C obtained 9 points total each.

How many subjects did they take in the examination, and what are the values of X, Y, Z?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 2 of 2 |

Altogether 40 points were awarded.

Each subject's total awarded points had to be at least 3+2+1=6 in order for the prize hierarchy to make sense.

Therefore, the total of 40 points could be in 5 subjects with 8 points each; no other way of factoring the 40 would conform to the previous two paragraphs.

The 8 points must be x=5, y=2 and z=1, rather than 4, 3, 1 respectively, in order for student A to have received 22 points total: 5+5+5+5+2.

At this point we have answered the questions posed in the puzzle. A matrix of the results shows:

                  recipient of given number of points
                  other subjects       English
1st place 5 pts.  A     A     A     A     B
2nd place 2 pts.  C     C     C     C     A
3rd place 1 pt.   B     B     B     B     C

  Posted by Charlie on 2013-11-20 13:11:37
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