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There are many free puzzles for the iPad...
I would suggest LetterPress, Where is My Perry, Quizboard, Trainyard Express, Checkers, A year of Riddles, Chess Hd, Flow Free
These are not specifically hard-core puzzles but a nice combination of challening word, quiz and board games as well. I think some of them come with in-app-purchases for buying coins or powerups but you can disable that by going to your iPad Settings to deactivate this feature.
There are a lot out there. You didn't mention how old the kids were; what would be fun for one age might well be frustrating for younger children.
Airport Mania: First Flight Lite. The Lite version is free, but it is worth getting the full version. This is a management game, really, where you have to match by color landing planes with the appropriate gate. As it progresses it gets more and more challenging, adding multiple runways, fuel, repairs and paint booths. It's not a pure puzzle game, but it is very, very fun. I actually downloaded this on WiiWare first, and wasn't expecting much, but my daughter and I both played it for hours.
Flow is fun, and there is a free version. It's easy at first, then starts to require a lot more thought.
Drop7 is kind of a number matching, tetris-ish game (that description doesn't do it justice). Free version available.
Genesis Free is a free version of a really colorful and cool looking puzzle/strategy game. Set in space, with some nice sounds. Eye candy, but still fun.
Don't forget all of the Bejeweled clones out there. They are pretty much all the same, but the classics are classics for a reason.
One game that isn't free but I highly, highly recommend is World of Goo. In my opinion, it is one of the best mobile games available, perhaps even THE best. It is a physics based building game that has spawned copies, but never been equaled. It costs $5, but it is well worth it and you won't have to deal with annoying push ads.