In a tennis tournament, there are 100 players. each match is played between two players. the winner advances and the loser is eliminated. assuming a minimum number of byes (games in which a player automatically advanced due to no opponent), how many matches need to be played to determine a winner?

To determine the winner is necessary to played 99 matches

Step-by-step explanation:

For determined the number of match, we are going to divide the game in rounds, every round is when every player plays with another and one advance and the other loses. That means that every round, the number of players is reduced to the half approximately. So:

Finally the number of matches that need to be played to determine the winner is the sum of matches that we can form in every round. That is:

50+25+12+6+3+2+1=99

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.