After teleporting to the eleventh floor, the conquerors found themselves in the middle of an arena. Then they got the mental message about how this floor was going to work.
Here they needed to fight challengers in the arena in one on one battle. Who would fight against whom would be chosen in a random order and the battle would be life and death battles. So to win it, one needed to kill the opponent.
It was possible that a single person would be chosen continuously if Rein's group's luck was bad and as it was a one on one battle, nobody would be able to assist the chosen person.
But as this was ultimately a fighting tournament, none of them were worried. They might not be very good in the field of war strategy, but when it came to fighting, all of them were confident in their capabilities to defeat any kind of opponents.