• Look for numbered squares that are very close to one another. If only one square separates two numbered squares, black out the square between them, since leaving it empty would connect the two numbers. If two numbered squares are diagonally adjacent, black out the two squares they both border.

• Look for 1s. Since they are going to be on an island that's only as large as the square they're in, you can immediately black out the four squares surrounding them.

• Take advantage of large numbers, particularly when they're near the edge of the puzzle or surrounded by other numbers. If the path of a large number is limited in one direction, you can assume the island must continue in the other direction.

• If there's a large open space in the grid, look for larger numbers that can reach that area. Since you can't have any 2x2 clusters of black squares, you can visualize which islands are necessary to fill in that area.

• Pay attention to places where a path (either black or white) must continue. Since the black squares must all be connected, a string of black squares that have only one possible outlet must continue through that outlet. The same is true for white squares, except you must remember that the islands will have a limited size and might not continue through those outlets.

• Watch for numbers in corners (both in the natural corner of the puzzle and corners made by black boxes). A 2 in a corner must connect one space either horizontally or vertically. In either case, the square diagonal to the 2 must be black (as the rule requiring a border on islands would force a black square there in both situations). Similarly, if you have a longer chain started that has only one square remaining, and it must branch off in one of two neighboring directions, you can black out the square between the two options.

• Don't forget about good old trial-and-error! If you get stuck, try marking a square as empty or filled and see where the puzzle goes from there. If you have an unresolved 2 available, try starting your experiment there, as you can usually solve that island by proving one direction wrong.

• For more solving tips and tricks, be sure to stop by Conceptis' Nurikabe page.

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