[pdurrant]

Originally Posted by Javed

Doesn't seem mathematical either to me. There must be some trick. Like a talking parrot that flies from one of the prisoners' windows to the other (outside the castle) and repeats what each wise man says.

No, there's no trick. No talking parrots, or any other communication through pets or wildlife.

Spoiler:

There a kind of slow communication, when they are not released from the tower each evening.