Though it probably couldn't be seen, given that he was still holding the Sorting Hat over his face like a mask, Kyle's expression quickly became one of disgust. Moving much more quickly than when he had turned the taps on, he hurriedly turned them off again.
Okay, so... probably not here then. That was... unbelievably frustrating, but Kyle tried to tell himself that it could also be a good thing, if he considered it from the perspective that he had ruled one possibility out.
'Tried' being the operative word, because more than anything else he felt annoyed that he hadn't worked out the answer as quick as he would have liked, and stressed because time was running out fast.
There was still a possibility that the probably-a-Gordian-Knot was here in the bathroom, hidden somewhere else, but Kyle decided to check elsewhere first. Still the most likely source of a noxious gas was the oven, especially now his main suspicions about the bathroom had been ruled out.
Turning left out of the bathroom, Kyle rounded the corner so that he faced the kitchen. The smell of the food nearby seemed to even permeate through the hat pressed against his face, so he figured that he might as well spare a moment to cast a Bubble-Head Charm. He took the hat away and pointed his wand at his face instead, moving it in a counter-clockwise motion
"Viseo Ebullio."
There, now if he did manage to trigger anything harmful on top of the stench of the rotten food and the Shrieking Shack in general, he'd be protected. Kyle had a lot of faith in the Bubble-Head Charm, as he used it all the time when brewing potions, especially when experimenting.
Looking down at the hat he now held in one hand, Kyle considered... everything. He was no longer thinking about putting the thing on and find out what his Hogwarts house would have been, but was instead tempted to ask it if it knew where the other clue was. But the thought crossed his mind only for a moment, because, when it came down to it, Kyle wanted to solve the riddle for himself. If the hat helped him - and, really, he didn't seriously believe that it would - then it would make his own accomplishments in this task null and void.
He needed to focus on the riddle, and not on the hat. Glancing at the oven in the kitchen, Kyle bit his lower lip uncertainly as he remembered that one line of the poem that had him completely stumped.
'... Wood it would deface.'
Was he even in the right place at all? He was starting to doubt himself, but knew he had to at least look so that he could count this location out too. Perhaps this was even some kind of joke that the challenge-makers were trying to make; getting warmer and warmer in terms of the clue... until they were literally looking inside an oven. That would be pretty amusing.
Stuffing the hat into the pocket of his robes, Kyle moved into the kitchen, bypassing the sink and crouching down in front of the oven, opening the door of it as he did so. He peered over the top of the stove, looked inside the main compartment of the oven, and eyed the dials at the top. Could it maybe be disguised as a dial, perhaps hidden behind one or in the place of one, unless it was actually hidden inside the oven. Kyle scanned the entire thing without attempting to turn any dials
just yet, making sure to look at every square inch of the appliance in case the item he was looking for happened to be in clear view.