"Modular arithmetic leading to group theory" can also lead to https://en.wikipedia.org/wiki/Polyominoes:_Puzzles,_Patterns... , which is the book that made a lot of theory CS click for me.

(The Cuisenaire colours would make a nice alternative to resistor colours for low-bandwidth covert channels. I enjoyed one of the Aubrey/Maturin books in which the ballroom has been decorated with the following signal flags: http://tmg110.tripod.com/SigFl/sig-1.gif , encouraging the maritime wallflowers who could read them to "engage the enemy more closely.")