1) The 2 can see itself and the 6 (2 squares); the rest of the squares (EE, N, W of it) must be water. The square NW of it must be water, or there is a checkerboard.
2) The 5 can see at most 3 squares on the vertical, so it must see at least 2 more on the horizontal; the square E of it must be land.
3) By the top 7, there must be three land squares visible to it on the top row. Therefore, there are three land squares visible horizontally to the 3; the square S of it must be water.
4) The only place where the oasis can be is the square S of the 3; squares NE, E, SE, S of it are land.
5) The 3, 4, and lower 7 can see their fill; that forces W of 4, S of 4, WW of 3, W of lower 7 to be water.
6) The 5 can only see 3 squares horizontally; the squares N and S of it must be land for it to see the full 5.
Solution to the sample
2) The 5 can see at most 3 squares on the vertical, so it must see at least 2 more on the horizontal; the square E of it must be land.
3) By the top 7, there must be three land squares visible to it on the top row. Therefore, there are three land squares visible horizontally to the 3; the square S of it must be water.
4) The only place where the oasis can be is the square S of the 3; squares NE, E, SE, S of it are land.
5) The 3, 4, and lower 7 can see their fill; that forces W of 4, S of 4, WW of 3, W of lower 7 to be water.
6) The 5 can only see 3 squares horizontally; the squares N and S of it must be land for it to see the full 5.
DONE.