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Special stages are a small stage with a massive amount of Rings in it. You have a Ring goal, for example, 200 rings, which you have to get in a certain time. The limit is listed at the bottom of the screen, and the ring goal is listed under the current ring count. Get all the rings, and you get a Chaos Emerald. Get all 7, and you can go Super if your character is capable of it, and you get a cool bonus at the end of the game, no matter what. When you are Super, you are invincible anything but instant death areas and drowning.