Ender's Game : Was Ender's Anton's key turned on?

If not, how could Ender be smarter than Bean?

Show me the holes!

No, and Ender isn't smarter than Bean, he is simply a better commander.

Ender did not have Anton's key. In the original books, Ender entered school ahead of Bean, not at the same time. Ender was naturally smart (which was why his parents were given permission to produce a "third" child. Bean was smarter than Ender, and was the backup choice if Ender couldn't produce. They were hoping they wouldn't have to use him, because they felt the other kids wouldn't take him seriously. He was behind the scenes calling most of the shots, including which kids were selected to be in Ender's army.