Jigsaw: Live or die. Make your choice. Let the game begin.
Jigsaw: Congratulations. You are still alive. Most people are so ungrateful to be alive. But not you. Not anymore.
Adam: My name is very fucking confused.
Adam: I don't give a crap if you covered yourself and had a 15 hooker gang bang.
Answer: Amanda was supposed to put the key around Adam's neck rather than just on his chest. If she had done so as instructed by Jigsaw, he would've been able to unlock his shackle and leave the bathroom. Adam was a voyeur, the irony being that if his key had been placed correctly around his neck, all he would've had to do would be to look around to find it. Adam's tape states, "what do voyeurs see when they look into the mirror, " so, again, it's a hint that all Adam would've had to do was look at himself. I noticed as well, Jigsaw says, "the key to that chain is in the bathtub." /IS/ in the bathtub. Not /was/. So Jigsaw probably thought Adam could still get out. He says, "so many people are ungrateful to be alive. But not you. Not anymore." So it's like, 'I have taught you this lesson, now you can go free because now you'll appreciate your life unlike you did before'.