Question

В розыгрыше кубка участвуют 256 команд . в кубковых матчах ничьих нет а проигравшая команда выбывает сколько всего матчей было проведено в розыгрыше этого кубка

Answer 1

Значит всего было 256 команд, т.е

1).256/2=128 

2.)128/2=64

3.)64/2=32  

4.)32/2=16

5)16/2=8    

6.)8/2=4  

7)7/2=2  2/2=1

8.)128+64+32+16+8+4+1=253
Ответ : 253 матчей было проведено в розыгрыше этого кубка.
Ещё можно решить эту задачу с х более простым способом, если таково решение не подойдёт я напишу как решать с х )) Успехов ! 

Answer 2

Calculation of the Total Number of Matches in the Cup

To calculate the total number of matches in the cup, we need to consider that there are 256 teams participating and no draws occur in the cup matches. Additionally, each losing team is eliminated from the competition.

Let's break down the calculation step by step:

1. In the first round, there are 256 teams. 2. In each round, half of the teams are eliminated. Therefore, the number of teams in each subsequent round is halved. 3. The cup continues until there is only one team left, which is the winner.

To calculate the total number of matches, we need to determine the number of rounds and the number of matches in each round.

Calculation of the Number of Rounds

Since the number of teams is halved in each round, we can calculate the number of rounds by finding the logarithm base 2 of the number of teams.

Let's calculate the number of rounds using the formula:

Number of Rounds = log2(Number of Teams)

In this case, the number of teams is 256, so:

Number of Rounds = log2(256) = 8

Therefore, there are 8 rounds in the cup.

Calculation of the Number of Matches in Each Round

To calculate the number of matches in each round, we can use the formula:

Number of Matches = Number of Teams / 2

Let's calculate the number of matches in each round for all 8 rounds:

Round 1: 256 teams / 2 = 128 matches Round 2: 128 teams / 2 = 64 matches Round 3: 64 teams / 2 = 32 matches Round 4: 32 teams / 2 = 16 matches Round 5: 16 teams / 2 = 8 matches Round 6: 8 teams / 2 = 4 matches Round 7: 4 teams / 2 = 2 matches Round 8: 2 teams / 2 = 1 match

Calculation of the Total Number of Matches

To calculate the total number of matches, we need to sum up the number of matches in each round:

Total Number of Matches = Sum of Matches in Each Round

Let's calculate the total number of matches:

Total Number of Matches = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 matches

Therefore, in the course of this cup, a total of 255 matches were played.