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Hitori rules

Hitori is a game played on a rectangular grid of numbers. The aim is to eliminate cells (by turning them black), so that the following rules are followed,
  1. Each row and column may only contain each number once. Note that this does not mean that a row or column has to contain any particular number.
  2. You can't have two black cells next to each other. Linked diagonally is fine.
  3. All the white squares must be one single connected whole, i.e. from any white starting square, you must be able to reach any other white square by only moving to adjacent white squares. Diagonal moves are not allowed.
A successfully completed Hitori puzzle,
From these rules we can make a few conclusions,