In the Chamber of Secrets, till the end, no one knows that the monster of Slytherin and the creature behind the attacks is a Basilisk.
Dumbledore, of all people, should have figured it out using the following clues
There are the following observations from which at least Dumbledore could figure out that the creature was a Basilisk:
Slytherin (and Riddle, perhaps?) being fond of snakes, it would be hard to miss that the monster of Slytherin would be snake-like at least.
There are presumably a limited number of magical creatures that can petrify their victims.
The fact that roosters were being found dead in suspicious circumstances was a clue to the Basilisk.
Plus, it wasn't a satisfactory explanation that an Acromantula killed Myrtle, as she was uninjured, but dead.
Surely Dumbledore could put two and two together and figure out what the monster was?
I believe the clues pretty much narrow it down to a Basilisk, correct me if I am wrong.
After all, even if it takes a genius to figure it out, Dumbledore was the right man for the job!
But he presumably didn't
I say this because:
He made no attempt to distribute mirrors among the students as a safety measure.
Nor did he station hundreds of roosters in the school to kill the basilisk.(Surely even Riddle would have a hard time killing so many roosters quickly to save his basilisk?) This would have been an effective measure, as roosters living as far away as near Hagrid's hut were threats to the Basilisk, so many roosters in the castle would probably get the job done.
Of course these methods are kind of extreme, but they are helpful in saving lives.
I can understand if no one else could figure out what Slytherin's monster was, but why couldn't Dumbledore do so?
After all, all it would take is some digging. Dumbledore, highly intelligent, would probably figure it out easily.
Can someone give me a reasonable explanation for this?