The tournament game in which number of teams participated is multiplied some 2 like 2, 4, 8, 16, -----, is considered.
It is expressed as N which is the number added all of several numbers that shows which round game is each game held on one tournament.
For example, when the number of teams is 8, the tournament becomes as shown in the figure.
As for the number of games, there are four games in the 1st round, two games in the 2nd round and one game in the 3rd round.
Therefore, when the number in ○ is added,
N = 1 + 1 + 1 + 1 + 2 + 2 + 3 = 11.
It is expressed as N which is the number added all of several numbers that shows which round game is each game held on one tournament.
For example, when the number of teams is 8, the tournament becomes as shown in the figure.
As for the number of games, there are four games in the 1st round, two games in the 2nd round and one game in the 3rd round.
Therefore, when the number in ○ is added,
N = 1 + 1 + 1 + 1 + 2 + 2 + 3 = 11.
(1) Find N in the tournament whose number of teams is 16.
(2) Find N in the tournament in which the 6th round game is the final game.
(3) N was 4083 in the tournament of a certain number of teams.
In the tournament of twice as many number of teams as this, N is to be 8178.
Find the number of teams when N is 4083.
(2) Find N in the tournament in which the 6th round game is the final game.
(3) N was 4083 in the tournament of a certain number of teams.
In the tournament of twice as many number of teams as this, N is to be 8178.
Find the number of teams when N is 4083.
Answer
(1) 26
(2) 120
(3) 2048
(2) 120
(3) 2048
