# When did the tournament start?

[Inspired by the movie Bloodsport]

The Kumite is an illegal underground fighting tournament organized in the typical single elimination bracket style. Think March Madness. All fights are fought one at a time on a central stage because the fighters want to watch other fighters to try to figure out their style in order to have a better chance at beating them.

The champion of the tournament, Frank Dux, did so with with 56 consecutive knockouts.

When did the tournament start?

Edit: This is only my second puzzle, and I think I kind of screwed up the presentation. Could have been a lot better. Lesson learned about taking time to think out my presentation.

• How long does a match last? What happens if there are an odd number of players? – f'' Feb 25 '16 at 0:22
• @f'' longest match ever was 1 minute 6 seconds. Shortest was 8 seconds. If there are an odd number then random drawing would determine who got a first round bye. There would not be bye's beyond the first round – Kevin Feb 25 '16 at 0:27
• Why wouldn't there be byes beyond the first round? – f'' Feb 25 '16 at 0:36
• That's the rules of the tournament. Just like how the NFL playoffs work. – Kevin Feb 25 '16 at 0:37
• If you think you've screwed up the presentation, no matter - rewrite it as an edit. If the presentation is so messed up that you'd get different answers, post the properly-written version as a new puzzle and link to it from here. – Lawrence Feb 25 '16 at 10:58

The fight is

(functionally) eternal.

because

If it's a single elimination bracket tournament, and he's one 56 consecutive matches, there must've been $2^{56}$ combatants... which is a lot.

Given each match occurs on a single stage, they're happening in serial. So unless each fight took less than 6 seconds, they would have had to have started before the birth of the universe.

That being said, let's assume you could find 72 quadrillion willing combatants, who also happened to be immortal (how else do they live long enough to survive the billions of years of waiting between fights)... If I, as the organiser, charge each of them a \$10 entry fee, that's 720 quadrillion dollars. Now assuming I was paid this at the start of the universe (I'm a smart business man and only accept up front payments), and invest the money in a term deposit at a measly 6% PA compounding... Now that the fight is over and I can pay Frank Dux his (very generous) \$1,000,000(!) prize money, I now have \$[computation time exceeded... lets assume it's lots...] at my disposal. ...and finally it's time to live out my dream and swim like Scrooge McDuck in a sea of gold coins that exceeds the size of the universe by many orders of magnitude. • Thanks to the possibility of first round byes, you can cut the required amount of combatants roughly by half. – f'' Feb 25 '16 at 2:12 • @f'' - well that makes my get rich exceedingly slowly scheme much easier, now I only need to retrospectively find 36 quadrillion combatants! ;) ...of course, in seriousness, that plus the other comments added to the question since I answered, could actually break things. If we did have exactly$2^{55}+2$combatants and Frank was (by exceedingly unlikely$1/(2^{54}+1)\$ chance) in the only round one bout, and all but one bout in history went for 8s (OP said they ranged from 8-66s), means we could technically have started anywhere up to 5 billion years after the start of the universe... – Alconja Feb 25 '16 at 2:27

3 minutes ago.

He knocked out all of the other fighters before the match started, and therefore won by default when no opponent could be found before the round timed out. Go Frank!