3. A tournament consists of matches between exactly three players, each, respectively, garnering 2 points, 1 point, and a zero score. The ones who obtained no score are eliminated and the rest are grouped into threes to engage again in matches, with possibly one or two players having a bye. If there are 999 players in the tournament, how many matches would have been played by the time a champion, the one who earned two points in the last match, is declared?
(ans. 997, which is equal to the number of players which earned a zero score in each of the 3 -person matches).