5 Simplified, with some Wikipedia references corrected, from the original puzzle. The intended solution is essentially the same.
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[Okay, I've given up on diagrams, at least for now, so here it is in words:]

Equivalent of weighing coins to findfinding three heaviest coins in order.

How to find the three best teams or individuals, in order, from a field of dozens?

Could be thought of as a gold medalweight, silver medal and bronze on a balance that holds one coin on each side.

Round-robin(Simplified, for instancewith some Wikipedia references corrected, can result in inconclusive loopsfrom the original puzzle. The intended solution is essentially the same:)

How to most efficiently and fairly determine gold, silver and bronze medalists from a field of 8 contestants who play one-on-one matches?

The challenge here, though,Talent is presumed to use the most efficient approachbe strictly ordered. that results in:A better contestant always beats any weaker one.
 Silver awardee was beaten The eventual gold medalist does not lose to anyone.
 The eventual silver medalist loses only byto gold awardeemedalist.
 Bronze awardee was only beaten by The eventual bronze medalist loses to silver medalist, possibly perhaps also to gold if they are in a match, awardee but wins every other match.
 Everyone else was beaten All other contestants lose to the silver medalist, or to another contestant who loses to silver, or to another contestant who loses to another who loses to silver, and so on.

The tournament need not have a predetermined number of matches. For the solution found by bronzethis puzzle's poser for 8 contestants, the worst case requires 11 matches while the best case requires 9 matches.

Round-robin, for instance, (possibly also gold and/or silver) awardeecan result in inconclusive loops is extremely inefficient. For 8 contestants, 28 matches are played.

A recent winter olympics play-off single knockout typeWinter Olympics event resultedused a hybrid approach that resulted in no medal for the presumed third third-best skier skier (Langenhorst?) becauseas she lost early in a one-and-out contest toto the eventual gold medalist during the single-elimination first stage. She She never got to challenge the eventual silver or bronze medalists medalists. The That unfair system as solution minimizes the averagehas a fixed number of 8 matches for the sake of fair results.:

Warning: The solution found by poser does not easily lend itself to "bracket" format as, for one thing, the number of matches is not predetermined.

[Okay, I've given up on diagrams, at least for now, so here it is in words:]

Equivalent of weighing coins to find three heaviest in order.

How to find the three best teams or individuals, in order, from a field of dozens?

Could be thought of as a gold medal, silver medal and bronze.

Round-robin, for instance, can result in inconclusive loops.

The challenge here, though, is to use the most efficient approach that results in:
 Silver awardee was beaten only by gold awardee.
 Bronze awardee was only beaten by silver, possibly also gold, awardee.
 Everyone else was beaten by bronze (possibly also gold and/or silver) awardee.

A recent winter olympics play-off single knockout type event resulted in no medal for the presumed third-best skier (Langenhorst?) because she lost early in a one-and-out contest to the eventual gold medalist. She never got to challenge the silver or bronze medalists. The system as solution minimizes the average number of matches for the sake of fair results.

Warning: The solution found by poser does not easily lend itself to "bracket" format as, for one thing, the number of matches is not predetermined.

Equivalent to finding three heaviest coins in order of weight, on a balance that holds one coin on each side.

(Simplified, with some Wikipedia references corrected, from the original puzzle. The intended solution is essentially the same:)

How to most efficiently and fairly determine gold, silver and bronze medalists from a field of 8 contestants who play one-on-one matches?

Talent is presumed to be strictly ordered. A better contestant always beats any weaker one.
 The eventual gold medalist does not lose to anyone.
 The eventual silver medalist loses only to gold medalist.
 The eventual bronze medalist loses to silver medalist, perhaps also to gold if they are in a match, but wins every other match.
 All other contestants lose to the silver medalist, or to another contestant who loses to silver, or to another contestant who loses to another who loses to silver, and so on.

The tournament need not have a predetermined number of matches. For the solution found by this puzzle's poser for 8 contestants, the worst case requires 11 matches while the best case requires 9 matches.

Round-robin, for instance, can result in inconclusive loops is extremely inefficient. For 8 contestants, 28 matches are played.

A recent Winter Olympics event used a hybrid approach that resulted in no medal for the presumed third-best skier (Langenhorst?) as she lost to the eventual gold medalist during the single-elimination first stage. She never got to challenge the eventual silver or bronze medalists. That unfair system has a fixed number of 8 matches:

4 Separate the challenge statement from the sentence about round-robins.
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Okay, i've given up on diagrams for this:[Okay, I've given up on diagrams, at least for now, so here it is in words:]

Equivalent of weighing coins to find three heaviest in order.

How to find the three best teams or individuals, in order, from a field of dozens?

Could be thought of as a gold medal, silver medal and bronze.

Round-robin, for instance, can result in inconclusive loops.

The challenge here, though, is to use the most efficient approach that results in:
 Silver awardee shouldwas beaten only by gold awardee.
 Bronze awardee shouldwas only be beaten by silver, possibly also gold., awardee.
 Everyone else should've beenwas beaten by bronze (possibly also gold and/or silver) awardee.

A recent winter olympics play-off type single knockout type event resulted in no medal for the presumed third-best skier (Langenhorst?) because she lost early in a one-and-out contest to the eventual gold medalist. She never got to challenge the silver or bronze medalists. The system as solution minimizes the average number of matches for the sake of fair results.

Warning: The solution found by poser does not easily lend itself to "bracket" format as, for one thing, the number of matches is not predetermined.

Okay, i've given up on diagrams for this:

Equivalent of weighing coins to find three heaviest in order.

How to find the three best teams or individuals, in order, from a field of dozens?

Could be thought of as a gold medal, silver medal and bronze.

Round-robin can result in inconclusive loops.
 Silver awardee should beaten only by gold awardee.
 Bronze awardee should only be beaten by silver, possibly also gold. awardee.
 Everyone else should've been beaten by bronze (possibly also gold and/or silver) awardee.

A recent winter olympics play-off type event resulted in no medal for the presumed third-best skier (Langenhorst?) because she lost early in a one-and-out contest to the eventual gold medalist. She never got to challenge the silver or bronze medalists. The system as solution minimizes the average number of matches for the sake of fair results.

Warning: The solution found by poser does not easily lend itself to "bracket" format.

[Okay, I've given up on diagrams, at least for now, so here it is in words:]

Equivalent of weighing coins to find three heaviest in order.

How to find the three best teams or individuals, in order, from a field of dozens?

Could be thought of as a gold medal, silver medal and bronze.

Round-robin, for instance, can result in inconclusive loops.

The challenge here, though, is to use the most efficient approach that results in:
 Silver awardee was beaten only by gold awardee.
 Bronze awardee was only beaten by silver, possibly also gold, awardee.
 Everyone else was beaten by bronze (possibly also gold and/or silver) awardee.

A recent winter olympics play-off single knockout type event resulted in no medal for the presumed third-best skier (Langenhorst?) because she lost early in a one-and-out contest to the eventual gold medalist. She never got to challenge the silver or bronze medalists. The system as solution minimizes the average number of matches for the sake of fair results.

Warning: The solution found by poser does not easily lend itself to "bracket" format as, for one thing, the number of matches is not predetermined.

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