If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7 and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Deven port reaches quarter finals?

Let total number of teams participated in tournament is n + 10
There are 10 teams 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 ? n(n + 1) = 20n ? 90 ? n² ? 21n + 90 = 0 hence n = 6 or 15
If n = 6, the top group 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 = 90/10 = 9. This is not possible. Hence n = 15. Then total number of teams is 10 + 15 = 25.

From the solution of previous question a team even with two wins can advanced to next stage where it has to play 3 matches so total number of matches is 5.

Consider top three team if they won maximum number of matches then points with them is 7 + 6 + 5 = 18, remaining 28 - 18 = 10 points can be distributed to bottom 5 teams, so even after getting 2 points or 2 wins a team can advanced to next stage by tie breaker rule.

From the solution of previous question even after winning 5 matches a team can get eliminated so to be sure a team must win 6 matches.

In the 1^st round in one group number of matches is (7 x 8/2) = 2
Lets consider bottom 3 they will have 3 matches between them, so remaining 28 - 3 = 25 matches have involvement of top 5 teams, if they won equal number of matches i.e 5 each then decision will be taken based on tie breaker rule, hence a team may be eliminated even after winning 5 matches.

If the top eight seeds make it to quarterfinals, then from the table we can find that Sharapova being top seed will meet seed 8 in the quarterfinals, and in the semifinals she will meet the winner of the match between seeds 4 and 5. So she will not meet seeds 4, 5 or 8 in the finals.
We can sum up the given information as below:
(ii) No team plays against the same team more than once
(iv) No ties permitted.
As per the information given for stage I, we can conclude and draw the table that
(a) As B lost at least one match, hence A won all the 3 matches.
(b) The two teams who lost all the matches cannot be A (as it won all 3 matches), cannot be B (since it is given that E lost to B), cannot be D (since D won against C & F). Hence, the two teams must be C and F.
(c) F did not play against the top team (i.e. A).
We can tabulate all the information as :
In the given below table a blank space means there was no match in this stage (i.e there was no match between A and E in this stage), Result of a match for a team is shown in its row,
(d) A lost both its matches against E and F.
(e) F won against A, hence is the bottom team (out of C and F) which won both the matches F won against C as well. This also means that C lost both its matches against B and F.
(f) Apart from A and C, one more team lost both the matches in Stage-II. That team can neither be E (since A lost to E), nor B (since C lost to B), nor F (as F won both its matches). Hence, the team must be D.

All odd numbered seeds up to 15 reach the 2nd round while instead of seeds 2 to 16 the players who reach the second round are seeds 31, 29, 27, 25, 23, 21, 19 and 17.
The second round matches are between seeds 1-17, 31-15, 3-19, 29-13, 5-21, 27-11, 7-23 and 25-9. Since there are no upsets in that round the winners are seeds 1, 15, 3, 13, 5, 11, 7 and 9.
The quarter final line up would be
1-9, 15-7, 3-11 and 13-5.
If seed 13 wins her match in the quarters she will next meet seed 1, i.e. Maria Sharapova in semifinals.

Maria Sharapova, seed 1, would meet the winner of the match between seed 8 and seed 9, but it is given that Serena Williams, seed 8 lost against seed 9 Nadia Petrovain the second round. Hence Nadia Petrova (seed 9).

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)
From the table Diesel team won against Edison.

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)
The new condition would be:
Initially total number of goals made by the teams are Bose (11), Diesel (9), Edison (= 5), Faraday (= 1), Marconi (= 7), and Rankin (= 4)
Now total number of goals made by the teams are Bose (5), Diesel (9), Edison (7), Faraday (4), Marconi (7), and Rankin (5)
So only Diesel and Marconi have the same number of goals.