Let's solve an example.

This is an example.

(1)
A shape of the room represented by a number 1 is already fixed.
Put four blocks and surround the room.

( A red mark means a cell in progress.)

(2)
Two numbers which adjoin in diagonal must be separated with two blocks.
A pair of numbers which place an blank cell in between and adjoin it must be also separated by a block.
Put the blocks to partition rooms into two.

(3)
As the area of the room is 3, to extend room like this is inevitable.

(4)
Enclose the fixed room with blocks.

(5)
If you put a floor panel on this cell, the isolated block could not be connected to any other block.
Put a block here to extend the wall instead of the floor panel.

(6)
Any room cannot reach to these cells no matter how floor panels are extended from a numbered cell.
It is not possible that the cells are filled by floor panels.
Fill each cell with a block.

(7)
Putting a block here makes a big square with four blocks.
It contradicts the rules.
To put a floor panel here is inevitable.

(8)
Two rooms have just been fixed.
Enclose these rooms with blocks.

(9)
A ... To pile four blocks is forbidden.
B ... Putting a block here makes a room without a number.

(10)
A ... Enclose the fixed room of the number 3 with blocks.
B ... To pile four blocks is forbidden.

(11)
Putting a floor panel on the cell A divide wall into two pieces by the line 3 - A - 1 , it prevent the wall connect all.
Putting a block here is correct.

(12)
A ... To pile four blocks is forbidden.
B ... Put a floor panel here to make the room of which area is four.
C ... Enclose the fixed room of the number 4 with a block.

(13)
If you put a floor panel on the cell A, the line contains number 3, number 4, the cell A and number 3 would divide the wall into two.
Put a block on the cell A instead of the floor panel.

(14)
Fill remaining square cells with floor panels and finish.

This is only a single instance of the solution methods.
There are many procedures which result in the solution.
Solve puzzles by yourself and discover theory of your own.
It is also one of the pleasure of this puzzle.

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