Logic puzzle grid thing

Starter puzzle

(Notes on interactive Java applet: click to change the colour of a square; press 'u' to undo, or 'c' to clear the grid and start from scratch).

Rules

You have to fill a grid with black or white cells, so that: there is one contiguous region of each colour; no 2x2 region is filled with a single colour; for each numbered cell, the number indicates how many squares of continuous colour there are along the row and the column starting at the numbered cell.

Taking that a little slower:

• You are given a grid, with some numbered cells that are filled in black or white.
• You must fill all the remaining cells either black or white.
• The finished grid must contain a single connected region of black and one of white. ie. from any black cell, you can get to any other black cell, without going over white cells or moving diagonally - and vice-versa.
• Within any 2x2 square, you can not colour all four cells the same colour.
• When any cell contains a number, that number indicates the total number of consecutive cells that have the same colour as the numbered cell, counting along the row and the column containing the numbered cell. In other words, this is a count of: the starting cell, plus the number of cells of the same colour directly to the left of that cell, plus the number directly above, directly to the right, and directly below that cell.

  Here's a small example of a completed 5x5 grid obeying these rules.

  For example, if you are given a white square containing the number '2', then that square and exactly one of its immediate neighbours is white. All other immediate neighbours of the square (excluding diagonals) must be black, and the next square beyond the white neighbour must be black.

  Here is an example of a completed grid:

  3
  	2
  		6

  Solution to sample puzzle

  Here's a walk-through of the solution to the puzzle at the top of this page.

  4
  	3

  (Stop reading now if you want to try to solve the puzzle yourself.)

  The white '4' in the top left corner indicates that there are a total of four white squares starting from that corner and going out to the right or down. In this case, there are two possibilities for the 4 white squares: the whole top row and one square below the '4', or the whole left column and one square to the right of the '4'. Either way, the squares to the right and below the 4 must be white:

  4
  	3

  Now we know that the square above the '3' must be black - otherwise we'd have a 2x2 region of white squares in the top left corner of the grid. The third black square is either to the left or the right of the '3' - we don't know which yet.

  Next, look at the square in the middle on the right. If it's black, then either the 2x2 square in the bottom right is all black, or there's an isolated island of white in the bottom right of the grid - either of which is bad - so we fill the square in white.

  4
  	3

  We now have two separate regions of white; the only way of joining them is for the top-right square to be white. That completes the set of white squares linked to the '4' in the top-left, so the bottom left must be black. Finally, the '3' is also complete, so the bottom-right square must be black:

  4
  	3

  Harder puzzles

  There are a few more hints at the bottom of the page, if you get stuck on these...

  
  

  7
  	4
  				8

  
  (Printable version)

  				9
  	2
  						3	3
  			6
  	3			2				7
  						3
  		7
  						7

  (Printable version)

  
  
  
  
  

  Enjoy!

  Hints

  SPOILERS alert!

  There are a few rules-of-thumb that can be deduced from the basic rules after a bit of playing.

  You should be able to figure these out for yourself: don't read them until you get completely stuck.

  If you are completely stuck, you might find that these help you:

  1. Cells of the same colour can't meet on a diagonal: (Otherwise there would be no way to connect the white cells without separating the black cells, and vice-versa).
  2. The squares around the border of the grid must either all be a single colour, or must consist of one run of each colour. (If you had multiple runs of the each colour, then any path that connected the two white runs would have to divide the black regions, and vice-versa).
  3. Starting from any cell that isn't on the border of the grid, there can be only one path to reach the border of the grid. (If there were two paths, they would create a loop, and this would isolate the squares inside the loop from those outside).
  4. If any cell contains a number, and it isn't on the border of the grid, the cells the contribute to the number can only include one cell that touches the border of the grid. (Otherwise you'd either create a loop, or two separate runs of the same colour on the border).