In Ender's Game, what are some quotes that show that Ender is intelligent? 

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clairewait | High School Teacher | (Level 1) Educator Emeritus

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Ender's intelligence is slowly revealed from the very beginning of his experience at battle school. It starts in his room, when he figures out how to use his desk almost immediately and with very few instructions. Later, in the game room, his intelligence is clear in how quickly he figures out one of the games:

Ender understood the regularities by then. Understood the rules the computer was following, so that he could always, once he mastered the controls, out maneuver the enemy (46).

When it comes to the point that the computer is only winning by being so fast he cannot physically keep up, Ender further proves his intelligence in taking on one of the older boys in a short battle. He demonstrates his intelligence, not only in the game itself, but in the set up of playing the best two out of three, so that he has a chance to figure out how to use the controls.

Later, Ender figures out how to crack the security of the individual students' desks, and wins a silent war in his launch group by anonymously attacking Bernard, a known bully.

He was not studying. He was telling his desk to keep sending a message into the interrupt queue every thirty seconds... (49)

Though he never overtly gives himself away, Alai later calls him out on figuring this out so quickly. He confronts Ender with:

Come on, who else? It sure wasn't Bernard...Doesn't matter. I found out how to fake a new student entry...I found something else out too. I can't do it with your name. (67)

The other students become aware of Ender's intelligence very quickly as well. This pattern continues throughout Battle School and into Command School.