| Solid Question -
14-07-2008, 11:18 PM
in yar 2008, 20 candidates across the world took part in the "World Mega Brainstar Championship". there were only two rounds in the event. in the first round, 20 puzzles were given to each contestant. for each correct answer, 2 points were given and for each incorrect answer, 1 point was deducted. no points were awarded or deducted for an unattempted puzzle. at the end of the first round, only the top ten contestants moved to the second and final round. in second round, these ten contestants played a round robin chess tournament, such that every contestant plays exactly one match with every other contestant., and in each match in this round, 2 points were awarded for a win and one point was deducted for a loss. there were no draws in this rounds. in any round (i.e either first or second) no two contestant scored the same number of points. at the end of any round, the cumulative total number of points scored by a contestant in all the rounds completed till then is called the net score of the contestant at the end of that round. the net score of a contestant at the end of all the rounds in the championship is called the final score of the contestant. it is known that no two contestants had the same net score at the end of the second round. finally the contestant with the highest score is crowned as the winner.
1) what can be the minimum possible final score of the winner?
2) at the end of the second round, if each of the ten contestants had a non negative score, then wat could have been the minimum possible score of the winner?
3) if the final score of the winner was 18 points, find the maximum possible net score of this contestant at the end of the first round? | 
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