Hermione had figured out who Peeves was. It was very obvious and she only doubted it at first because it was an unlikely column for this particular person to write. Ron had to be stupider than she originally thought to not see it. He read Ask Peeves at least once a day!
Dumbledore was listening to people's arguments about who Peeves was the next mourning. (It was Saturday therefore there were no classes.) One person went into the Great Hall at a time to present their reasoning. Ron had obviously shown up too, and Hermione asked, "Who do you think it is?"
"No question, it's Snape. I figured put it had to be a teacher here, and Snape sounds most like Peeves: always pissed off. I'm surprised to see you here, Hermione. Who do you think Peeves is?"
"Oh, you'll find out. I'm sure I can get you in to meet Peeves once I guess correctly."
"What're you talking about?"
"It's so obvious who this 'Peeves' is, but I know you don't know and no one else is obsessed with Ask Peeves as you, so they wouldn't know either."
Hermione and Ron fought about the identity of Peeves until it was Hermione's turn to go in. She told Dumbledore who it was, knowing she was right.
"I got it!" Hermione said excitedly after classes later that day. She had opened a letter brought to the Gryffindor common room by an owl. "I've won the meet Peeves thing, and it says I can bring two friends to meet him too! We meet him right after dinner tonight in the Dumbledore's office, I think Dumbledore will probably introduce us."
Ron would've argued that he should've won as he was Peeves' number one fan, but he was speechless. He couldn't eat at all during dinner, feeling as though he would puke it up if he tried.
When at last the plates had cleared from the tables, Harry, Ron, and Hermione went to the gargoyle that guarded Dumbledore's office. It moved away letting them past without any password. They approached the door and they heard Dumbledore say, "Come in, Peeves is ready to meet with you."
Ron slowly pushed the door open, wondering who he would face inside.