Little late to the party, but the solution is as follows:
1) Arrange the correct order for the top row (tiles 1, 2, 3, 4)
2) Then arrange the tiles for the first column (tiles 5, 9, and 13)
3) then finish the 2nd row (tiles 6, 7, 8)
4) same for the 3rd row (10, 11, 12)
5) finally the last row (14, 15)