Since there are 8 teams and we know that 8 = 23 hence there are 3 rounds in 2nd stage.
The team which gets 1 point at 1st stage would be eliminated because the combination may be 6 points for the team and 2 times each for remaining. There are some more cases that supports the idea.
The total score is 40 points. If each team scores equally, each team scores 40/5 = 8 points
Each match has 4 points and each team plays 4 matches. Hence total number of points is 40
Paraguay wins all matches. So it scores 3 x 4 = 12 points.
Turkey loses all matches. So it scores 1 x 4 = 4 points.
16 points are scored by Turkey and Paraguay
The other teams score 40 - 16 = 24 points
As all other teams score equal points, each team scores 24/3 = 8 points
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) ? (5 + 9 + 7 + 4 + 5) = 37 ? 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is casued only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 ? 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
Out of 9 matches only 1 match end up with tie so total number of points is 8 × 3 + 2 = 26
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) ? (5 + 9 + 7 + 4 + 5) = 37 ? 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is caused only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 ? 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
Since total number of points is 26 so number of points more than 2.6 but less than 5.2 is (i.e points 3. 4, 5) 5.
From the discussion above we can say that. It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.
Let total number of teams participated in tournament is n + 10
There are 10 terms in the bottom group then n teams in the top group. It is given that the bottom group gets 45 points since we have 1 point per match therefore 45 matches playing amongst themselves. Therefore they should get 45 points from their matches against the top group i.e., 45 out of the 10n points. The top group get nC2 points from the matches among themselves. They also get 10n - 45 points against the bottom group, which is half their total points.
Hence nC2 = 10n - 45 or n(n + 1) = 20n - 90 or n2 - 21n + 90 = 0 hence n = 6 or 15
If n = 6, the top ground would get nC2 + 10n - 45 = nC2 + 10(6) - 45 = 30 points, or an average of 5 points per team, while the bottom group would get (45 + 45) / 10 or an average of 9. This is not possible.
Hence n = 15. Then total number of teams is 10 + 15 = 25.
Spain beat New Zealand by 4 goal to 0.
Germany beat Spain by 2 goals to 1.
Spain
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