George found a new board game to play, which is sort of like sudoku in nature, but only has nine equal squres. The objective of the game is to fill each square with a number between 1 and 9 such that the sum of the numbers on each row, each columnn and each diagonal equal 15. Additionally, the numbers in all the squres must be distinct. Use integer linear programming to help George determine the correct assignment of numbers to squres.