If you mean to "*make a game with the same game rules and logic, but with new code & new graphics*", then yes, you can.

Copyright protects an expression of an idea, but not the idea itself. In the context of game development, an *idea* can be tic-tac-toe game. I write a webpage with JavaScript to play the game, that is my *expression*. You cannot reproduce my webpage without my consent, but you are free to code an exact replica of the game say, in iOS.

To prevent someone from making a game with the exact (or very similar) rules, you'd need a patent. Two famous games which are patented is "[Monopoly][1]" (they got the name right!) and [Tetris][2]*. There is a reason why you see people making many Reversi, Sudoku, Tic-Tac-Toe etc implementations.

<sub>*Technically, Tetris is not protected by patent, only by copyright. Many developers have [rejected the company's copyright infringement claims][3] as game design is not covered by copyright.</sub>


  [1]: https://en.wikipedia.org/wiki/Monopoly_(game)
  [2]: https://en.wikipedia.org/wiki/Tetris
  [3]: https://en.wikipedia.org/wiki/The_Tetris_Company