On myKindle Fire, my new favorite is Unolingo. Not sure if it is available on iPad.
Unolingo presents you with a partially filled crossword puzzle, with no clues, and you fill in the blanks with letters A-Z to complete the puzzle.
My favorite game for years has been Sherlock, which is available on iPad, but I think it plays better on PC, with a mouse.
Sherlock is similar to solving the sort of brain-teaser puzzles that give you a series of clues, like, "There are five people seated at a table, Mr Green is seated to the left of the man wearing the red tie, the man wearing the black tie is two seats to the left of the man with the blue shirt, etc...." and you have to figure out who is seated at which position.
I also enjoy Sudoku.