Cast Detect Curse and Detect Magic

After examining the crowns for a bit longer you decide that you won't get anywhere with just looking. You need to do something – but at the same time you are hesitant about touching them because they could be cursed... fortunately you have a way to find out just that.

Wasting no time you cast Detect Curse, and are pleasantly surprised to discover that you detect no curses anywhere near you – even the dark crown with the dim purple glow is not cursed.

Next you cast Detect Magic, and confirm your suspicions that the crowns are all enchanted. To your surprise there are eight other spots that are clearly magical – more so than the rest of the Arena, anyway. There's one such spot in the middle of each wall. Could it be... hidden doors? You begin examining the walls and after some careful searching you manage to locate eight doors, all of them hidden by illusions. It takes quite some effort due to your limited magic skills, but eventually you manage to dispel the illusions and reveal the doors. Each one is made from some white stone and with a symbol engraved on it. Unfortunately the symbols change roughly once every ten seconds. You watch the doors for a bit and see a number of different symbols: An arrow, an axe, a shield, a spear, a flower, a star, a teardrop, a book, a coin, a star again, a lake, a cloud, a star (different from the previous two), a flame, a mountain, an eye, a bow, a dagger, a chair, a cloak, a sword and shield, a mace, and a tree. Finally you get tired of it and stop watching the doors.

So it is either do something with one of the crowns, or try one of the doors. Decisions, decision...