SQUARE ROUTES: One solution method: In the bottom row, the two missing numbers must add up to 27 to make 30. Among the unused numbers, the only possible pair is 12 and 15. But which goes in which spot? Consider that if 15 is in the bottom right-hand corner, you would need an 8 in the right-hand column to bring that column’s sum to 30. But you can’t use 8, since it’s already in the grid. So 15 must be in the bottom left-hand corner and 12 in the bottom right. Because you now know 3 of the 4 numbers in the left- and right-hand columns, filling in the other blank in each of those columns is easy, and so is filling in the rest of the grid.