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Counting each pairing once in a round-robin tournament

Five entrants in a single round-robin tournament each have four opponents. That looks like 20 matches until you notice that A against B and B against A describe the same meeting. Counting each pair once gives 10 matches, a different question from how many rounds or days the event needs.

3–5 min

Questions you could explore

  • What changes if every pair plays twice instead?
  • Why does adding every entrant's opponent count count each match twice?

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Sports and games

Why can a quick chess move earn you extra time?

Imagine two chess clocks that each offer five seconds per move. One adds time to your balance; another delays the countdown without saving unused seconds. Explore how increment and delay reward quick play differently, even when their allowances look alike.

3–5 min

Why can a quick chess move earn you extra time?

Sports and games3–5 minImagine two chess clocks that each offer five seconds per move. One adds time to your balance; another delays the countdown without saving unused seconds. Explore how increment and delay reward quick play differently, even when their allowances look alike.

Sports and games

How many matches does a knockout tournament need?

A 127-player single-elimination tournament needs a schedule even though its opening bracket is not a neat power of two. Can you work out the number of matches without drawing every round? Look for something each completed match changes, then test whether byes affect the count.

2–3 min

How many matches does a knockout tournament need?

Sports and games2–3 minA 127-player single-elimination tournament needs a schedule even though its opening bracket is not a neat power of two. Can you work out the number of matches without drawing every round? Look for something each completed match changes, then test whether byes affect the count.

Sports and games

An offside position is only part of the rule

Fans shouting at a soccer match often wave their arms the moment an attacking player appears closer to goal than the defenders. Under the Laws of the Game, however, merely standing in an offside position is not an offense by itself: involvement in active play matters too. Position is assessed when a teammate plays or touches the ball, with additional details and exceptions in the rule.

4–5 min

An offside position is only part of the rule

Sports and games4–5 minFans shouting at a soccer match often wave their arms the moment an attacking player appears closer to goal than the defenders. Under the Laws of the Game, however, merely standing in an offside position is not an offense by itself: involvement in active play matters too. Position is assessed when a teammate plays or touches the ball, with additional details and exceptions in the rule.

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