Gee, when I was 11, I wrote a very basic password cracking program to break into a school computer (never ended up running it, but I wrote one - impressed the hell out of some of my friends at the time :-)
Re^2: How to introduce 8 year olds to (Perl) programming?
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We're talking Apple IIc computers :-) Maybe I was a bit older than 11, but thats what sticks in my mind at the moment. Also wrote a role-playing game in BASIC about that same time too. It did work. Though, I admit, I had help from my dad.