Summary: Investigating A Single-Elimination Tournament

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Part A: Investigating a single-elimination tournament 1. Given that there are 16 teams in the round of 16, how many teams will go forward to the quarter-finals 8 semi-finals 4 The final? 2 2. Describe how you found the number of teams at each stage. Here is an example, if two teams play against each other it equals 1 winning team, so if we begin with 16 teams, we follow the same rule. Divide 16 into 2 or half the number to give us 8 teams into the next round. The winning team of each match goes onto the quarter rounds, while the team that lost is eliminated. Similarly with the semi-finals, to go through it again though it would be easier just to divide the number (in this case 4) in 2, which the answer is 2. 3. Could a single-elimination tournament begin with any number of teams? Explain your answer. …show more content…

I guess that another reason for yes is because, even with numbers that aren't in the power of two tournaments can begin and end with any number of teams, there are only disadvantages such as some teams having to play more matches, while other teams have their first match in the second round. 4. A single-elimination tournament begins with n teams. What can you say about the value of n? Using algebra describe how to find the number of teams going into each round of the tournament. The value of n can be virtually any number. It is in the power of two and if it is not a multiple of 16 then some of the teams may have to go through some 'bye' rounds, which, as described earlier, means that some teams have to miss out on one round. n teams will go into the first round. h teams will go into the quarter finals. d teams will go into the semi

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