Anita prepared a fixture based on the league competition. She distributed this fixture to the coaches of all the teams. When Khushi received this fixture, it was misprinted and showed only the matches of rounds three and four. According to the above statement, study the fixture given below.
Answer the following Questions based on the above fixture and your prior knowledge:
Question: 1
In which round the match between number 4 and 3 teams will be held?
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In a standard cyclic scheduling system with $N$ teams (where $N$ is odd), team $A$ plays team $B$ in the round $R$ that satisfies the modular condition: $(A + B - 1) \pmod N$. Here, $(4 + 3 - 1) = 6 \pmod 7$, which matches the first round configuration.
When the number of teams ($N$) is odd in a league format, each team needs one round to sit out on a “Bye”. Because every team must take a turn resting, the total number of rounds always equals $N$.
To verify your work quickly: notice that the team receiving a bye decreases by 1 each round (Round 3 $\rightarrow$ Team 5, Round 4 $\rightarrow$ Team 4, Round 5 $\rightarrow$ Team 3, Round 6 $\rightarrow$ Team 2).
How many matches will be played in the above fixture?
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Alternatively, you can multiply the number of matches per round by the total number of rounds. With 7 rounds and 3 active matches per round (since 1 of the 4 slots is a Bye), $7 \times 3 = 21$ matches.
