Q.The number of rounds in a league tournament of 8 teams, played by the cyclic method, is:

Cyclic Tournament Scheduling

Think about a round-robin tournament — the kind where every team plays every other team exactly once. Now imagine you have to schedule all those matches across several days or weeks, with each team playing exactly one match per round. That's the core problem. Cyclic tournament scheduling is the method of arranging those matches in a repeating, predictable pattern so that the schedule is fair, balanced, and easy to generate.

The basic intuition comes from a simple observation: if you have an even number of teams, you can fix one team in place and rotate the others around it in a circle. Each rotation produces one round of matches. This is why it's called "cyclic" — the schedule cycles through all possible pairings by rotating the positions.

The Precise Meaning

In a cyclic tournament schedule, the matches are arranged in rounds. In each round, every team plays exactly once. The schedule is generated by a fixed rotation pattern, usually with one team held stationary (the "anchor") and the others moving around it. For an odd number of teams, a "bye" (a dummy team) is added to make the count even, and the team that would play the bye gets a rest that round.

The key properties are:

• Every team plays every other team exactly once
• Each round has the same number of matches (half the number of teams, rounded down)
• The schedule is deterministic — given the number of teams, you can generate it mechanically
• It is fair — no team gets an advantage from the order of matches

Why It Matters

This method is not just a mathematical curiosity. It is the standard way to schedule tournaments in sports leagues, chess tournaments, and even some corporate events. The cyclic pattern ensures that the schedule is balanced: no team has to play two matches in a row while another rests, and the spacing between matches against strong opponents is roughly equal for everyone.

A Concrete Example Without Numbers

Imagine you have six teams. You arrange them in a circle, with one team fixed at the center. In the first round, each team plays the team directly opposite it. Then you rotate all the teams (except the fixed one) one position clockwise. That gives you the second round. You keep rotating until every team has played every other team. The result is a schedule that is easy to produce, easy to verify, and fair to all participants.

Common Variations

There are two main ways to implement the cyclic method: …