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This is an example of a completed Fillomino grid. The aim in a Fillomino puzzle is to divide the grid in
to groups. The number in each cell tell you how many cells are in that group. Cells in group are
linked horizontally or vertically.

At the start of a Fillomino puzzle you will have some cells that are filled, some of these cells may
make up part of the same group, or they may not. You will not need to create new groups - you will
always be given at least one number for each group.

This is an example of a starting Fillomino grid. You can see that we have been given some clues, but we
still have plenty of cells left to fill!

I have highlighted 4 cells at the bottom of this puzzle, there is only one way for these cells to
expand, and this is upwards.

You will notice that as we complete groups, all the cells in that group will turn from white to colour.

We also have a highlighted '2' that can only extend in one direction on the left side of this puzzle,
and this is downwards.

We also have cells 'A' and 'B', these are currently empty, but the only groups that can reach these
cells are the '6' group. In the case of cell 'A', there is no other group that can reach this cell -
they are all too far away. In the case of cell 'B', it is surrounded by '6' clues - the '1' to the right
can't expand, so this must be a '6' as well.

We will now look at the highlighted '3'. We know that we need another 2 cells to complete this group.
Cell 'B' may or may not be a '3', we don't know yet. Either way, we still need one more cell to
complete this group. The only way this '3' can expand is upwards, so cell 'A' must be a '3'.

We can apply the same logic to the highlighted '6' clue. Again, cell 'B' may or may not be a '6', but
either way we still need another 4 cells to make up this group. The only other way this '6' can expand
is downwards through cells 'C', 'D' and 'E'.

The highlighted '5' can only expand upwards in to cell 'C', and the highlighted '4' can only expand to
the right in to cells 'A' and 'B'.

We can also look at the highlighted '3' clue on the right side of this grid. We know we need to add
another two cells to this group. This group might expand downwards in to cell 'E', but that still
leaves us needing to add another cell. That means we must expand in to cell 'D'. We don't know about
cell 'E' yet, but we'll find out soon.

We can apply the same technique to this set of highlighted cells.

- The highlighted '3' can expand in to cell 'A', but that still leaves it needing one more cell to complete the group. This can only be cell 'B'.
- The highlighted '5' needs two more cells, one of these might cell 'C', but that would still leave us needing one more cell. Cell 'D' must be a '5'.
- The highlighted '4' needs three more cells, this might be cells 'E' and 'F'. This would still leave us needing one more cell, and if 'E' and 'F' are filled with '4', this would only leave cell 'G'.

We can apply the same techniques to the highlighted '6' and '4'. We know that the highlighted '6' needs
another five cells. It might expand in to cell 'A', but that would still mean it needs to expand in
to cell 'B'. We can insert a '6' in to cell 'B'. It might now expand in to cell 'C', but that would
still leave this group needing another two cells. This leaves cells 'D' and 'E', i.e. they must be '6'
as well.

Looking at the highlighted '4', this group might expand in to cells 'F' and 'G', but that still leaves
us needing one more cell. The only option is cell 'H', i.e. cell 'H' must be a '4'.

We can now look at the highlighted '3', this group needs two more cells, but there are only two more
cells available to it, i.e. cells 'A' and 'B' must be filled with '3'.

The highlighted '2' can only expand in to cell 'C'.

The highlighted '8' can only expand in to cell 'D'. This group still needs another six cells, but it's
harder to come to any more conclusions here because of the other '8' clues in this grid.

The highlighted '8' needs another seven cells, it has single cells it can expand in to the left, down
and right, but it must expand upwards as well, i.e. cell 'A' must be a '8'.

The highlighted '6' needs another five cells. It has two cells to the left, but it must also expand
downwards, i.e. cell 'B' must be a '6'.

We don't have too much further to go in this puzzle now, and the grid is starting to close up. The two
highlighted '4' cells need another two cells, the only cells available to it are cells 'A' and 'B', i.e.
cells 'A' and 'B' must be '4'.

The highlighted '8' needs another seven cells. There is not enough space available to it, without
joining the other '8' group, i.e. cells 'C' and 'D' must be '8'.

Looking at the highlighted '5' clue, this can only expand in to cell 'A'.

It can sometimes be useful to look to see which groups could reach a particular cell. This is one of
those times! Looking at cell 'B', the '6' group is complete, so we can't add this cell to that group.
The '3' groups to the left can't reach this cell - it would make this group too big. The only group
that can reach this cell is the '8' group, i.e. cell 'B' must be a '8'.

Looking at the highlighted '4', there isn't enough space to expand here, so cell 'C' must be a '4'.

Looking at the highlighted '4' clue,l there are only four cells here for this clue to expand in to, i.e.
cells 'A', 'B' and 'C' must all be '4'.

Looking at cell 'D', this must be part of the '3' group to it's left and down.

Looking at the highlighted '3' clue, this is the only group that can reach cell 'E' now, and it's only
option is to expand downwards in to cell 'F' after that, i.e. cells 'E' and 'F' must be a '3'.

We can now fill in the remaining cells in this Fillomino puzzle,

- Cell 'A' must be a '3'.
- Cell 'B' must be a '6'.
- Cell 'C' must be a '3'.
- Cell 'D' must be a '6'.
- Cell 'E' must be a '4'.
- Cell 'F' must be a '3'.

Our completed puzzle!

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Hitori

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