An example of interactive puzzle done right is Snap: The Interlocking Dragon Making Game. But my kids just call it Snap. Gameswright publishes a lot of kid's games here in the good ol' USA.
Out of the huge overabundance I am directly familiar with Hisssss!, Castle Keep and Forbidden Island. Snap easily beats any of these games in enjoyability for both kids and adults. I find myself returning to this simple puzzle again and again.
Much like Hisssss!, Carcassonne or the ill-fated Rivers, Roads and Rails, Snap is a game about laying down tiles and matching up pictures. It's not just an art activity or jigsaw puzzle, though. Unlike more than half those games (and exactly like one of those games) you are scoring points competitively against actual opponents.
Each complete dragon earns you valuable victory points. After you successfully complete a dragon (must have at least 1 head and 1 tail), you score 1 point for a single "snap" and 2 points per "snap" for larger dragons. A snap is their simple term for the connection between two pieces. So if your dragon loops back onto the same piece, you count the connections, not the pieces.
Tigers are special tiles that let you re-score any tile you can fit them into, allowing you to cash in again on particularly high-value dragons.
Each player has a hand of 3 cards. You draw after you play a tile, allowing you to consider all your options while your opponent plays.
And those are the rules!
The innovations of Snap:
1) The jigsaw puzzle pieces. I don't know of any other tile-laying games with an interlocking design. Jigsaw puzzle pieces are awesome because the game stays put together, no matter how much you bump the sides or try to pull tiles out of alignment. I have seen mishaps that would cause an Irrecoverable Game State in Carcassonne instead not hurt Snap in the slightest.
2) The scoring. A point here and two points there might not seem like much. But Snap rewards two kinds of play with this victory point system. Firstly, a working strategy is to try to grab as many single point dragons as you can, keeping your hand cards fairly open to capitalize on available open heads or tails as they arise. But secondly, there are much higher scoring opportunities involving a certain amount of risk. You can steal someone else's dragon that they are working on. But it also might be a smart play to continue building a dragon when you have exactly the card you need to score big points on the next turn. I think it is an excellent educational opportunity for kids to offer up both paths to victory and let their minds stew in it.
3) The notepad. Someone went seriously old school and threw a small notepad + pencil in here for keeping score. The only question I have is why don't people do this more often? The cost of a standard generic pad+pencil is probably competitive to printing up a lousy victory track. Plus you also instantly have a record of every game of Snap you've every played!
Yes, this game has been played a few times.
Plus I have a record of my son's handwriting from when he was 5, how cool is that?
4) Bridging the gap between jigsaw puzzles and games. My 2-year-old daughter does not play Snap competitively. But she loves Snap because she also loves jigsaw puzzles. Along with Tsuro, Snap is the great leap from puzzles to actual game play and she is slowly making it. We take turns and she loves making dragons.
X) The jigsaw puzzle pieces. One reason more games probably don't use jigsaw pieces is durability. Jigsaw pieces by design create friction at each connection point. Add in rough treatment from kids and every tile starts to look beat-up after a while. The cardboard starts to separate and eventually the teeth bend until you have to smash them back into place.
If you want to lay tiles and score some points with kids, there is no better game. Much like most tile laying games, for short attention spans you can just cut the pile of tiles in half and thusly play to an earlier conclusion. Kids love making dragons. And they love scoring points to show their superiority over the great lumbering dad. Keeping track of points is not a problem with the handy scorepad. And turns do not last very long, as long as you have your plan made up when the other players are going.
Snap was designed by a guy named P. Joseph Shumaker, who deserves more accolades then he probably received for this game. Snap is certainly his masterpiece. A+