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Games and Tournament                                                                                279
                Now we can complete the table for Stage-II.      14.  (c) In stage 2 total points are 56.
                         A     B    C     D     E    F                Consider bottom 3 players, they must play  three
                    A    X                      L    L                matches among themselves  and  hence  they have
                                                                      minimum 6 points with them,
                    B          X    W     W                           Remaining points  56-6 = 50 if equally  divided
                    C          L     X               L                between top 5 then one would get 10 points, so
                    D          L          X     L                     to guarantee a seat in semifinal Ricky Singh has to
                    E    W                W     X                     score 12 points.
                    F    W          W                X           15.  (d) Total number of matches are as follows:

                Hence we can answer the questions now-                Stage I: 24
            9.  (e)                                                   Stage II: 24
            10.  (b)                                                  And required ratio is 1:1
            11.  (d)                                             16.  (c) Total number of matches are as follows-
            12.  (e)                                                  Stage I: 24
            Solutions for 13-17 :                                     Stage II: 24
            In stage I, in a group in total 6 matches and that will have      Semifinal: 2
                                                                           rd
            12 points in total. Total number of matches in this stage      For 3  place (Looser of semi final): 1
            is 4 × 6 = 24                                             Final: 1
            In stage II, total 8 players and they play each other except      Total number of matches is 52  and hence total
            a player who comes from same group but point of their     number of points is 52 × 2 = 104
            match in stage I is carried forward hence in stage II total   17.  (b) In stage 1 a player has to win minimum 1 match
            points is 28 × 2 = 56.                                    to advance to the next stage.
            Number of matches in stage II is 7 × 8/2 – 4 = 24         Now consider the different groups,
            13.  (a) In this case we have to minimize the points scored      South Kolkata: 1, 8, 9, 16 [seed 9 can advance after
                by 4th  ranker (Who advanced  to Semi Final). In      beating seed 16 without an upset]
                order to minimize the points scored by Ricky Singh      North Kolkata: 2, 7, 10, 15 [seed 10 can advance
                top three players should get maximum points, Let      after beating seed 15 without an upset]
                points achieved by top three player  at the end  of      Central Kolkata: 3, 6, 11, 14 [seed 11 can advance
                stage II is 14, 12 and 10 summing up to 14 + 12       after beating seed 14 without an upset]
                + 10 = 36 and remaining points 56-36 = 20 got         Saltlake: 4, 5,  12,13  [seed 12  can advance  after
                distributed to bottom 5 players.                      beating seed 113 without an upset]
                To minimize  the points  scored by Ricky Singh,  all      So seed 12 is the lowest seed who can advance to
                of the bottom five got same point (20/5 = 4 points)   stage II without causing Upset in stage I, and can win
                and with complex tie breaker Ricky is advanced to     the tournament [Please note here that in stage II or
                Semifinal.                                            semifinal there may be an Upset

            From the given information we can draw following table.

                          Amit     Bhanu     Chandra    Dripto     Eshan     Firoz    Gandhi    Hemant
              Amit         X                               W                                                 7
              Bhanu                  X                     L                   W
              Chandra                           X                    L                             W         2
              Dripto        L        W                     X
              Eshan                             W                    X                   L
              Firoz                   L                                        X                   L         0
              Gandhi                                                 W                   X
              Hemant                            L                              W                   X
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