Seven chess players, ranked from 1 to 7, based on their ratings before the tournament, took part in a double round robin league tournament, where each player played two games against every other player, i.e., one game with black pieces and the other with white pieces. These matches were scheduled on consecutive days, and that exactly three matches were scheduled on every day, involving six of these seven players, while the remaining player will be rested on that day and no particular order is followed for resting the players.
For any player, one point was awarded for a win, half a point for a draw and zero points for a loss. The person with the highest total number of total points at the end of the tournament is said to have finished first, the one with the next highest total points, second and so on. If two or more players end with the same total number of total points, their ranks before the tournament are considered and the one with the best rank (i.e., the numerically lowest rank) before the tournament is considered to have finished ahead of the other player/s.
1. For how many days did the tournament take place?
(1) 11 (2) 12 (3) 13 (4) 14 (5) 15
2. Which of the following cannot be the total number of points of the player who finished first?
(1) 6.0 (2) 7.0 (3) 8.0 (4) 9.0
(5) None o f these
3. If exactly one player ended with the highest total number of points, what is the minimum possible difference between the points of the player who finished first and that of the player who finished last in the tournament?
(1) 0.5 (2) 1.0 (3) 1.5 (4) 2.0 (5) 2.5
4. If the winner had 9.5 points, which of the following can be the number of points scored by the player who finished last?
(1) 7.5 (2) 6.5 (3) 5.5 (4) 4.5
(5) More than one of the above
5. At the end of the tournament, it was found that only players A and B finished with the same number of points and no other pair of players from the seven players finished with the same number of points. What is the minimum possible total number of points of the person who finished first?
(1) 6.5 (2) 7.0 (3) 7.5 (4) 8.0 (5) 8.5