Well then, can he arrange for that to happen without having to stand here holding it? Is there perhaps a convenient hole in the wall or the floor to support this?

Yep, now that he's looking for it, he spots a little hole in the stone floor below each crystal. Once there's a color-coded rod in each slot, merrily sparking at its corresponding crystal, the room's lighting is considerably more psychedelic. 

This does not appear to have an obvious effect on the floating pillow-mattress-thing and its waving tassel, nor does the room seem to be otherwise changed. 

He really expected that to work. It would have been too easy though he supposes. What to try next? Well, he just tried to sit on the pillow before. What happens if he tries to lift it?

Well, if he grabs the bottom of one side and tries to pull it up, it seems to resist being lifted just like it resists falling down. 

Well, there's still other things he can try.

Maybe if he sits on it and tries pulling up on the tassels. Come to think of it he now heavily suspects that whatever the control scheme works when you're on it.

Pulling up on the big central tassel causes the giant pillow-thing to rise! And, more generally, it moves in the direction he tugs the tassel, up to maybe a running pace.

He can now glide across to the alcove on the pillow, if he so chooses.

... He really should have investigated the pillow more first. Oh well, he got there in the end. Now he has to decide if he wants to bring some of the rods from the previous trial with him. After a few seconds of thought he decides on yes and goes back to collect another two rods and then he guides the flying pillow up to the doorway.

It's a little bit awkward to keep the rods pointed at not-him and not-the-flammable-pillow but he can manage if he tries. 

This door is also unlocked! It opens into an L-shaped hallway lit by windows overlooking the river, which in turn terminates in a smaller wooden door. 

By solving a difficult puzzle using mathematical reasoning, you have gained 1 Artes Liberales XP! 
By completing the Trials of the School of Many Towers, you have gained 1 Might XP! 

He'll dismiss the notification and continue onwards to the door.

It opens into a slightly dusty courtyard containing several large pieces of furniture and two men in dark wool tunics, one short and stocky with a wide leather tool belt and the other taller and younger-looking with hastily rolled-up sleeves. The first spots Alex entering the courtyard and waves him over.

What's Alex doing with the spark-rods? 

He is going to try to make sure they don't point anywhere they could cause a problem and otherwise try to act like it's normal to be carrying sparking rods around. He expects the men will have an opinion when he goes over to talk with them.

He expects correctly.

Tool Belt starts speaking as soon as Alex is in earshot. "You the new one from the street posting? Grab the other — ack!" He is interrupted by an orange spark shooting out of a rod and skittering across the cobblestone, and his expression goes from intent to furious. "Blast it, man, are you insane, stealing artifacts from the magi? You trying to get us all whipped?" 

Sleeves Up refrains from commenting for the time being, eyeing Alex suspiciously from the other side of a finely-carved pine dresser. 

"I'm a new student. It sounds like you think something else is happening?"

"A new — what were you doing in the servants' quarters then?" His tone is wary, now, but still suspicious. (A further sputter from one of the rods doesn't help. Both men wince.) 

"The what? The place I just came from was a series of puzzles."

"A series of what...That door you just walked out of leads to the scullery and laborers' —" a nearly simultaneous pair of orange and blue sparks interrupts him again, "— bunks. Ah, blight it, this is above my pay grade. Leave the furniture, Theve, we're escorting this fellow to Pellia. She'll know what to do with 'im. You, come with me, and keep those things pointed at the ground," he adds to Alex. 

"I can do that." He will indeed ba careful about the rods even if a part of him really wants to check if the door is indeed going to another place than where he thought.

The as-yet-unintroduced laborer leads Alex to a different door, Theve bringing up the rear while keeping a nervous distance from the sparks. This close, Alex notes they both seem to have the same shade of dark grey hem to their tunics.

Several corridors and a spiral staircase later, they're knocking on an office door and a woman's voice says, "Enter." 

As the three of them file in, Alex notes the layout of what appears to be a small personal office. It's taken up mostly by a large wooden desk and a set of shelves containing scores of labeled ledgers and a single clay figurine of a gryphon on the top shelf. One window in the back overlooks a larger courtyard. There's a marked slate and an open ledger on the desk, a small iron box against the wall, and an enormous ring of keys hanging by the door. 

An aged and severe-looking woman sits at the desk; she's wearing the same shade of grey as the laborers' hems. She looks up from the desk with a frown. "Cossus, good to see you, how goes the furnishing for Magus Murena's — what in the Hells was that?" The sparks strike again.

Cossus only slightly flinches this time. "Fella says he's a new student," he replies. "Got some kinda magic wands on 'im." He says this in the tone of someone still deeply unconvinced they weren't filched from somewhere.

"They were elements in what I thought was an entrance exam involving a hedge maze, the moat and a puzzle involving these wands. I was expecting to be met by a professor when I finished. Given that I wasn't, I'm questioning the circumstances of me undertaking those tests. The Fae running the moat portion seemed to confirm it was the faculty who gave him his task."

Pellia gives him a sharp look when he starts talking about an entrance exam, and by the time he finishes it's practically lacerating.

"Fae in the moat, my arthritic kneecaps," Cossus grumbles. "You think we're dense? Grawtosh doesn't even have a moat." 

"Not entirely true," says Pellia. The other two staaaaare. 

Pellia stands and walks around to the front of her desk, eyes still firmly on Alex. "Hand over the wands, please. Carefully," she adds, with a glance towards her highly flammable surroundings.

"Alright." He carefully hands them over.

Careful to keep them aimed downwards at all times, Pellia taps each wand thrice against the wall. No more sparks issue therefrom. 

"You say that you are a new student? Do you have any documents to that effect?"

"I have a letter of introduction from a mage from the Order of Dreams."