Once you finish off Dai, you will proceed across the courtyard and into the room, where you will fight::

~Hayate~

"Hmph! YOU WILL NOT PASS!"
Weapons: Long Sword x1
Sand Sheild-Hayate will stomp on the ground, making a shield of sand pick off the ground and harden, forming a sheild. Can block attacks that cause 50 dmg or less / lasts four posts
Sand Blow-Hayate will swing his blade upward at his opponent while swinging the other downward at his foe. 50 damage
Sand Crush-Hayate will hold his arm toward his opponent, opening the palm, and a hand made of sun will rise out the ground, grabbing them. He will then start to close his palm, while the sand hand does the same, crushing the foe. 75 damage
If the battle is won~
Prize(s): $66
Sealed Scroll
"No..I lost.."
If the battle is lost~
Prize(s): X
"Hmph. Disgusting."

If there's someone in it, it's not empty. You need to work on your maths.
Also, you're fighting him. I don't have a real weapon, and, when/where do we meet Rei?
She appears somewhere halfway through the series...

I put empty room because..it SEEMS like no one is in it.

Yeah, well...
NYAH NYAH.