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Grades 3–5 · Mathematics

How can four teams all play one another without a repeated match?

A round-robin schedule gives each team a match against every other team. With four teams named A, B, C and D, each team needs three opponents. Counting each team’s list separately would count every match twice.

G037 visual explanationThree rounds contain all six distinct pairs; Round 1; A — B; C — D; Round 2; A — C; B — D; Round 3; A — D; B — C; each team appears once per round; Fictional teams: every pair meets exactly once.Three rounds contain all six distinct pairsRound 1A — BC — DRound 2A — CB — DRound 3A — DB — Ceach team appears once per roundFictional teams: every pair meets exactly once.

In the diagramThree rounds contain all six distinct pairsRound 1A — BC — DRound 2A — CB — DRound 3A — DB — Ceach team appears once per roundFictional teams: every pair meets exactly once.

Three illustrated rounds contain AB and CD, AC and BD, then AD and BC; all six different pairs appear once.

A plays B is the same match as B plays A. Listing each pair only once gives six matches altogether. The scheduler must then arrange those pairs so that no team is required in two places at once.

One possible first round is A against B and C against D. The second can pair A with C and B with D. The third pairs A with D and B with C. Every team appears once in each round.

Together, the three rounds include all six different pairs. This works if two playing spaces are available at once. Real schedules may need extra rules, but the example shows how pairing and timing solve different parts of the same organizing problem.

About this explanation

Starting knowledge: Recognize a pair of teams and know that one team cannot play two matches at the same time.

Sources

  • NRICH, University of Cambridge — Round-Robin Scheduling
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