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I'm trying to find the total points of each competitor of the Triwizard Tournament after the second task.

“They will be marked on how well they perform each of the Tournament tasks and the champion with the highest total after task three will win the Triwizard Cup.”

Points from each Task:

           Cedric   Fleur    Harry    Viktor
Task Ⅰ       38   35–39?   40     40
Task Ⅱ       47      25    45       40
Task Ⅲ        0       0       50        0

Harry and Cedric both had 85 points after the second task, and Viktor had 80 points, but how many did Fleur have if she still had a “fighting chance” to win the tournament after the second task?

  • Fleur needs minimum of 36 points total after Task Ⅱ, to win if Task Ⅲ winner gets 50 points and others none. – Oni Feb 28 at 16:07
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    There are no points for the third task, the first to the cup wins the contest. Giving points for the task would be pointless. – QuestionAuthority Feb 28 at 18:58
  • Why then say "the highest total after task three will win the Triwizard Cup.". – Oni Feb 28 at 19:01
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    @QuestionAuthority Bagman says: “A maze. The third task’s really very straightforward. The Triwizard Cup will be placed in the center of the maze. The first champion to touch it will receive full marks.” And Cedric says: “The one who reaches the cup first gets the points. – Alex Feb 28 at 20:15
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It's impossible to say for certain what her actual score was. However, it seems likely that it was between 60 and 64.

The highest score she could have possibly had was 64 points.

We know that Harry and Krum were tied for first place after the first task, with 40 points (Harry received scores of eight, nine, nine, ten and four in the first task):

'You're tied in first place, Harry! You and Krum!' said Charlie Weasley, hurrying to meet them as they set off back towards the school.
Harry Potter and the Goblet of Fire, Chapter 20 - The First Task

The most Fleur could have possibly scored in the first task is therefore 39 points. With the 25 points we know she got in the second task, that would put her total after the first two tasks at 64 points.

The lowest score she could have possibly had was 36 points. This would require the winner of the third task to receive fifty points, and the others to receive none. However, as there'd seem to be no means of identifying who came second, third and fourth once the Cup had been touched by the winner, this is the most likely situation.

A total of 36 points after the second task would have required her to score 11 points on the first. That would be a particularly bad performance, and would have no doubt been mentioned. As it wasn't, I think we can rule out the possibility of a low score in the first task.

From Ron's description of the four Champions' attempts at the first task, Fleur likely received a similar score to Cedric (who seemed to suffer the worst injuries during that task). A total of 60 would require a score of 35 on the first task, which is an average of 7 per judge.

  • Though her performance for the first task was really poor - she never managed to get her sister and wasn't even able to defend herself while trying – Nikita Neganov Feb 28 at 18:30
  • @NikitaNeganov That was the second task, which is why she only got 25 points (out of 50). She did considerably better in the first based on Ron's description. – Anthony Grist Feb 28 at 19:08
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    This assumes that the cup is worth 50 points, which might not be the case. – Alex Feb 28 at 20:17
  • @AnthonyGrist yup, my bad – Nikita Neganov Mar 1 at 4:16

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