I am surprised no one has mentioned Monument Valley on iOS or Android. I played it a bit in front of 4 years old and they were instantly hooked. Of course, they will need bunch of hints and help to get through all the levels but it's almost an ideal logic puzzle game I have ever encountered. I also started playing tic-tac-toe where I lose randomly to keep things interesting :). It is surprisingly not easy to teach all rules of tic-tax-toe to (perhaps many) 4 year old. The trick was to show them I play it against computer on iPad for lots of games.