"This is the count of the Armies of the Djinn, that gathered to pay homage to their Lord.
On the first day, the Army of the City of Brass assembled; of steelshod mortal warriors, a Legion, of companies as many in rank as in file, and there were as many companies as there were files in every company; with them, the fearsome Ghuls of the Earth, in like but greater array; and when they were mustered as one, their General, Ghulgast of the Mist, stood with them, so that all together were as many in rank as in file; and all paid homage to the Lord of the Djinn.
On the second day, the Army of Mount Kaf assembled; of steelshod mortal warriors, a Legion, as many as the day before; with them, the flamegirt Ifrits of the Air, in like but greater array than the Ghuls that went before them; and when they were mustered as one, their General, Shahrokh of the Flame, stood with them, so that all together were as many in rank as in file; and all paid homage to the Lord of the Djinn.
On the third day, the Army of the Sunken Continent of Mu assembled; of steelshod mortal warriors, a Legion, as many as the day before; with them, the mighty Marids of the Sea, in like but greater array than the Ifrits, that went before them; and when they were mustered as one, their General, Dandan of the Deep, stood with them, so that all together were as many in rank as in file; and all paid homage to the Lord of the Djinn..."
To cut a long story short, these three armies are followed by an additional four (incidentally, the Army of Shadow, led by Amir Aamon; the Army of the Secret Flame, led by Amir Bael; the Army of Lilith, led by "her paramour Sammael"; and last, the Lord's High Guard, led by the Sultan of Qamorah) each of the same pattern and each larger than its predecessors.
What is the count of the Armies of the Djinn?
Bonus Question (hard): Show that more than one solution is possible; or show the contrary.
Draft solution.
