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Quiz Results III (Posted on 2014-02-10) Difficulty: 3 of 5
Each of the five students - Andy, Danny, Ellen, Janice and Sammy received different marks in a mathematics quiz which was held last week. Students who made correct statements had obtained higher scores than those who made incorrect statements.

The following are the statements made by the five students:

Sammy: Andy and Ellen gained the top two places.
Janice: No, what Sammy just said is incorrect.
Danny: I was ranked in between Sammy and Janice.
Andy: Janice came second.
Janice: I had obtained a lower score than Ellen.
Ellen: Exactly three of the previous five statements are correct.

Determine the order in which the five students finished.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts I beat myself regularly | Comment 3 of 4 |
Ah yes, I see.

I had considered the possibility that maybe Janice made a correct and an incorrect statement, but I considered it too late in my logic, and thus concluded that it was not the case.  I was pleased that my faulty logic led me to believe that it was not the case, as I think it is a contradiction.

Here is the logic that I should have used:

"Students that made a correct statement obtained higher scores than those that made incorrect statements".  If Janice made one correct and one incorrect statement, then Janice obtained a higher score than Janice.  But Janice only obtained one score, so this is a contradiction.

So, even having seen Charlie's posting, I think that there is only one solution.

Edited on February 10, 2014, 1:57 pm
  Posted by Steve Herman on 2014-02-10 13:38:41

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