One I did when I was much younger was after a trip to a Cracker Barrel restaurant. They have these golf tee peg games (triangle shaped board with holes and golf tees inserted). There are rules for doing jumps and removing pegs, with the goal of getting down to 1 peg remaining.

So I went home, fired up basica on my PCjr, and wrote a brute-force solver for it. Turns out there something like tens of thousands of possible solutions.

Then it became a challenge, to filter out duplicates (each solution appears 3 times if you apply it to the board with each 120 degree rotation, plus you have mirrors of these, etc). Was an amazing feeling for a youngster getting into computers.