My kids and I worked through most of "The puzzle ninjas" by Alex Bellos, and some of the "Pencil puzzles" books from Nikoli. Working on them with others, it's a lot of making little conjectures, testing (proving) the conjectures, and then applying them to various parts of the puzzles. Occasionally we've even used the fact that there is a unique solution to eliminate various possibilities.

They provide a bit of the satisfaction that finishing a good graduate math course homework set does.