## Nurikabe Puzzle

**How to Solve Nurikabe Puzzles**

This is a Nurikabe Puzzle.

It was created by Dr Gareth Moore of puzzlemix.com

The puzzle rules and a solving tutorial are here.

What follows is a walkthrough guide to solving the above puzzle.

Different numbers can’t touch each other, so fill in blocks where it wouldn’t be possible to put a number without it touching a different number.

There is now only one possible place to complete the 2 group in the bottom right corner. We can also place an extra piece in the 3 group above it.

The 2 group in the bottom left is complete so we know that all orthogonal squares must be filled.

The rule that says that all filled squares must be contiguous means we can fill in the square above the 3 we just added. Otherwise the square beneath the 4 would have been isolated.

There is now only one way left we could complete the 3 group, so we add the remaining 3 and fill in the horizontally and vertically adjacent squares.

There are some squares (marked with a white dot) that we can fill in that could not be part of any of the groups as they are too far away.

The no block of black squares rule means that we can fill in the 2 at the bottom centre of the board. As that completes the block of 2 we can also fill in the horizontally and vertically adjacent squares.

The contiguous black squares rule tells us that we must fill in the marked square so that the squares in the bottom right corner do not become isolated.

The bottom left corner must be a 3. It cannot be filled in as otherwise the remaining parts of the 3 group would cause it to become isolated.

The no block of squares rule tells us that we must fill in the square marked with a black dot. The 3 group is the only group that could reach far enough to fill this square.

We can complete the group and fill in the horizontally and vertically adjacent squares.

The no block of squares rule allows us to complete the bottom left corner of the puzzle.

The marked square is filled as it is unreachable by any other group.

There is only one direction the 5 group at the top of the board could start to be filled in.

This could have been done in step 3) had we spotted it.

The marked square can be filled in as it cannot be a number. If it were a number it would cause

an isolated area of black squares to be created in the upper right corner.

The no block of squares rule tells us that at least one of the marked squares must be filled in. The only number we could fill either one in with is a 4. We can automatically fill the right hand square as we know that either it or the one to the left of it is filled. If the left one is filled then the right one would also be filled.

The top right square is filled in as it is no longer reachable by the 4 group. We also fill in the marked square beneath the 2. It must be filled as if it were a digit we would create an isolated area of black squares in the top right corner.

This allows us to complete the 2 group and fill in the adjacent black square.

We can now fill in the marked square to join the black squares in the top right corner to

the rest of the filled squares.

There is now only one way to complete the four group and adjacent black squares.

We can fill another unreachable square (marked).

The no block of squares rule allows us to complete the 3 group in the upper left corner.

The no block of squares rule allows us to fill in one of the 5 group.

25) The marked square must be filled in as otherwise the black squares in the upper left corner would be isolated. Note that although the upper left squares could be joined by filling the two squares above the marked square, this would cause a 5 to be cut off from the rest of the group of 5’s.

No block of squares rule allows us to fill in another 5.

The final 5 must be filled in to join the 5’s into a single group and the remaining square can be filled to complete the puzzle.