In Chapter 4 of Harry Potter and the Half-Blood Prince, do we know why Dumbledore immediately knew that Horace was the armchair?
Please, I am looking for a different answer than "Dumbledore is brilliant." It takes a bit more than mere brilliance to correctly guess exactly what to poke in a room full of furniture.
My guess is that it simply looked out of place, either because it didn't match the rest of the decor (it was patterned on Slughorn's pyjamas, hardly the most common material used for an armchair), because he'd neglected to cover himself in the same dragonsblood spatter or was just too clean in general.
Cushions lay deflated, feathers oozing from slashes in their sides; fragments of glass and china lay like powder over everything. Dumbledore raised his wand even higher, so that its light was thrown upon the walls, where something darkly red and glutinous was spattered over the wallpaper. Harry’s small intake of breath made Dumbledore look round.
Dumbledore states that he knew that Slughorn was still in the house because of the lack of a dark mark and he would also be aware of his skill in transformation. Seeing that the armchair is the only thing mentioned that would be large enough to accommodate him, in hindsight it seemed the obvious choice.
‘What gave it away?’ he grunted as he staggered to his feet, still rubbing his lower belly. He seemed remarkably unabashed for a man who had just been discovered pretending to be an armchair. ‘My dear Horace,’ said Dumbledore, looking amused, ‘if the Death Eaters really had come to call, the Dark Mark would have been set over the house.’ The wizard clapped a pudgy hand to his vast forehead. ‘The Dark Mark,’ he muttered. ‘Knew there was something … ah well. Wouldn’t have had time, anyway. I’d only just put the finishing touches to my upholstery when you entered the room.’
Dumbledore later shows an ability to sense powerful magic. He detects a cleverly concealed entrance simply by murmuring a few words and touching it.
Harry did not ask how Dumbledore knew. He had never seen a wizard work things out like this, simply by looking and touching; but Harry had long since learned that bangs and smoke were more often the marks of ineptitude than expertise.
And although I appreciate you're asking questions about the book and not the film, it's certainly worth pointing out it was a little easier in the cinematic version given that armchairs don't usually have feet sticking out from under them :-)
There are three main hints:
The pattern of the chair matched Slughorn's taste in pajamas.
Dumbledore knew Slughorn for some years, he probably knew his taste/habits.
Dumbledore knew Slughorn's habits.
It was probably not hard for Dumbledore to figure out what Slughorn would disguise himself as.
Most importantly: The chair was the only thing left intact.
The whole room was absolutely out of order, (Dragon-)blood everywhere, furniture broken. The only piece intact and not stained was the chair, because Slughorn transformed himself after making chaos.
There were feet sticking out of the bottom of the armchair, and it was the only thing left intact. Albus also knew Horace’s style and it matched the pattern on the armchair, and Albus also knew that Horace would probably transfigure into a piece of furniture.
