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Tackle These Three Tests (Posted on 2005-08-07) Difficulty: 3 of 5
Arthur, Bert and Charles took three exams. In all exams, the first got X points, the second Y points, and the third Z points, X, Y and Z being positive integers such that X>Y>Z.

Summing the three results, Albert got 20 points; Bert, 10; and Charles, 9. Albert was 2nd in Algebra. Who was 2nd in Geometry?

  Submitted by Old Original Oskar!    
Rating: 2.7778 (9 votes)
Solution: (Hide)
Charles was 2nd in the other two exams.

The total number of points is 20+10+9=39, so X+Y+Z=13. If someone got three first places, he would have got at least 20 points, so 3X≥20 or X>6. In a similar way, if someone had got three third places, he couldn't have more than 9, so 3Z≤9 or Z≤3. Thus, the only possible values for (X,Y,Z) are (7,5,1), (7,4,2), (8,4,1), (8,3,2), and (9,2,1).

* (7,5,1) or (8,3,2) don't allow Bert getting 10 points.
* (7,4,2) or (9,2,1) don't allow Charles getting 9 points.

So, the only possibility is (8,4,1) and then Albert managed two 1sts and a 2nd (in Algebra), Bert had a 1st and two 3rds, and Charles got two 2nds (thus, Geometry) and a 3rd.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle AnswerK Sengupta2023-08-20 23:54:41
Some Thoughtsre: Albert?K Sengupta2023-02-04 00:05:20
solutionsalil2006-02-20 08:34:25
not enough infobo2005-08-24 18:44:25
re(3): Solution assuming that Albert is Arthur's real name...Bob Smith2005-08-08 17:18:23
Some Thoughtsre(2): Solution assuming that Albert is Arthur's real name...e.g.2005-08-08 14:55:13
re: Solution assuming that Albert is Arthur's real name...Bob Smith2005-08-08 13:34:07
SolutionSolution assuming that Albert is Arthur's real name...Charlie2005-08-07 03:37:50
QuestionAlbert?Richard2005-08-07 02:57:17
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