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After watching Rakudai Kishi no Cavalry, I found myself confused by what seems to be a plot hole. Specifically, the anime depicts the qualifying matches at Hagun academy for the Seven Stars Sword Art tournament. The qualifying matches seem to be a 20-round single-elimination tournament with 6 winners. This is never outright stated, but many points of dialogue suggest this rather strongly, and at the very least it is stated explicitly in the last episode of the anime that all of the competitors on the last day had won 19 matches.

The 6 winners:

The 6 winners

By basic math, a single-elimination tournament with 6 winners and 20 rounds would imply that there are about 6.3 million entrants to the qualifying tournament. That number of students at the school seems to be effectively impossible. For comparison, the population of New York City is about 8 million people, and the total number of high school students in Japan in 2011 was about 3.5 million. So this seems unreasonably large as an absolute number.

In addition, the number is too large relative to the size of the school. The area of Hagun Academy is said to be more than 10 times the size of the Tokyo Dome (according to http://rakudai-kishi.wikia.com/wiki/Hagun_Academy); using that figure, the average population density would be about 5 people per square meter (more than 100 times as dense as the most dense city in the world). In addition, we've gotten aerial shots of the school, and while large, it isn't nearly big enough to contain that many people.

Aerial shot from episode 12

So, I'm wondering, is this really the right number of students at the school? If not, is there some explanation for how the tournament has 20 rounds, or is this just a plot hole?

Logan M
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  • Certainly it is Single Elimination for Representatives, but i don't see anything about what happens when you loose. It would make sense that you have to continue fighting anyway, but it would be for prestige and the ability to knock other representative candidates out. – Ryan Mar 28 '16 at 15:52

1 Answers1

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  1. Hagun Academy (破軍学園 Hagun Gakuen) is one of the seven Mage Knight schools -> there are only 7 schools.

  2. We have a rule

With the competition, six students defeat 10 different students earning them their spot as Hagun Academy’s representatives for the festival.

So looks like we have less students in Hagun.

BTW, it's LN logic !!!

Chris Maverick
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  • For 20 rounds, it should be 2^20, not 2^19. If there were 1 round, it should be 12 students, not 6. It seems that I used the wrong figure for the area of the Tokyo dome, though yours isn't right either; it should be 112,456 m^2 for the whole site. But no matter how you fiddle with the numbers it comes out to at least 1 people per square meter, which would represent a dense (standing room only) crowd everywhere on campus, with no empty spaces (clearly not what's shown)... – Logan M Dec 26 '15 at 05:02
  • At 5 people per square meter there is serious risk of being crushed or stampedes occuring, and that would be the average crowd everywhere on campus. Simply put, based on what we're shown in the anime, it seems unlikely that the density is much more than 100-200,000 people per square kilometer, and it's much more likely to be below 50,000 /km^2. In any case, none of this solves the issue that a single school with that many students would be completely impossible to administrate and manage. – Logan M Dec 26 '15 at 05:04
  • ok, i edited my answer, sorry :D – Chris Maverick Dec 26 '15 at 07:22
  • Please make your answer consistent by replacing the wrong number with the correct figure. Please refrain from adding "Edit" addendum when the main content is wrong. – nhahtdh Dec 28 '15 at 11:35