Tic Tac Toe
To save on time and effort I used the base react-native hello world application and added the tic tac toe code, I was only to test it on Android.
For the solution checking I decided that creating a solutions file would be the quickest for the approach of solving the game board.
For the mechanics I went with the game always starting with X's then alternating from there.
For the layout I went with a simple grid and a header bar that told the user who's turn it is.