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→Classification: The example given is about 3rd place, not the losers of qfs
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Without any additional matches, the only position a single-elimination tournament can reliably determine is first - for example, if sorting the numbers 1-4 ascending, if 4 and 3 meet in the first round, 3 and 1 will lose in the first round and 2 will lose in the second, selecting 4 as the largest number in the set, but insufficient comparisons have been performed to determine which is greater, 2 or 3. Despite this, the candidate that loses in the final round is commonly considered to have taken second place (in this case, 2). When matches are held to determine places or prizes lower than first and second, these typically include a match between the losers of the semifinal matches called [[third place playoff]]s, the winner therein placing third and the loser fourth. Many Olympic single-elimination tournaments feature the bronze medal match if they do not award bronze medals to both losing semifinalists. The [[FIFA World Cup]] has long featured the third place match (since [[1934 FIFA World Cup|1934]]), though the [[UEFA Euro]] has not held one since the [[Euro 1980|1980 edition]]. | Without any additional matches, the only position a single-elimination tournament can reliably determine is first - for example, if sorting the numbers 1-4 ascending, if 4 and 3 meet in the first round, 3 and 1 will lose in the first round and 2 will lose in the second, selecting 4 as the largest number in the set, but insufficient comparisons have been performed to determine which is greater, 2 or 3. Despite this, the candidate that loses in the final round is commonly considered to have taken second place (in this case, 2). When matches are held to determine places or prizes lower than first and second, these typically include a match between the losers of the semifinal matches called [[third place playoff]]s, the winner therein placing third and the loser fourth. Many Olympic single-elimination tournaments feature the bronze medal match if they do not award bronze medals to both losing semifinalists. The [[FIFA World Cup]] has long featured the third place match (since [[1934 FIFA World Cup|1934]]), though the [[UEFA Euro]] has not held one since the [[Euro 1980|1980 edition]]. | ||
Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth to eighth places | Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth to eighth places. In one scenario, two "consolation semifinal" matches may be conducted, with the winners of these then facing off to determine fifth and sixth places and the losers playing for seventh and eighth; those are used often in qualifying tournaments where only the top five teams advance to the next round; or some method of ranking the four quarterfinal losers might be employed, in which case only one round of additional matches would be held among them, the two highest-ranked therein then playing for fifth and sixth places and the two lowest for seventh and eighth. | ||
The number of distinct ways of arranging a single-elimination tournament (as an abstract structure, prior to seeding the players into the tournament) is given by the [[Wedderburn–Etherington number]]s.<ref>{{citation | The number of distinct ways of arranging a single-elimination tournament (as an abstract structure, prior to seeding the players into the tournament) is given by the [[Wedderburn–Etherington number]]s.<ref>{{citation | ||