I really like loopy. It has a very stat mech or discrete math feel. I think it could be used to introduce deeper concepts in mathematics to novices, such as proofs, and the question of whether mathematics is constructed or discovered. A lot of the time solving loopy involves noticing re-usable patterns. But how do you know a possible pattern is re-usable? Well, you can prove it, such as with notions from graph theory…
Other puzzles I like in this collection that have such provable patterns are Pearl, Slant, Tents, Undead and Unruly. And, of course, Mines.