A topic very much like this one makes up a chapter in the wonderful book Godel, Escher, Bach http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

Two characters are in a race: one to build an impervious record player, the other to design a record that - when played - sets up feedback in the record player sufficient to destroy it.

It's a stunningly simple intro to a fairly deep topic: NP completeness, input validation, etc.