Shikaku is a type of puzzle made by nikoli. Watch out for this blog, since quite a bunch of Shikaku puzzles in this blog will feature the Unknown twist!
There are only two types of cells, a given cell and a blank cell. A cell with a question mark is a given cell. The objective is to divide the grid into some rectangles.
The interactions are simple. The grid must be divided into some rectangles such that each rectangle contains exactly one given cell, and its area is equal to the number in that given cell. For question marks (unknown given), you are only told that the cell is a given cell, but you are not told about the area of the rectangle this cell belongs to.
Divide (partition) the grid into some rectangles such that each rectangle contains one given cell, and its area is equal to the given cell. A square is also a rectangle.
Walkthrough of the example
The easiest part is the 1. It is obvious that the rectangle which the 1 belongs is that cell only, R3C4.
Next, the 4 in R4C3. A rectangle with an area of 4 can be either 1×4, 2×2, or 4×1. By trying each possibility, we get that the rectangle with the 4 must be 4×1; that is, R4C1 – R4C4.
Next, the 4 in R2C3. Same like the 4 in R4C3, we can try each possibility and get that the rectangle this 4 belongs to is R1C3 – R2C4.
Now, note R3C3. It can only belong to the 2. So the rectangle with the 2 is R3C2 – R3C3. By similar reasoning, R3C1 belongs to R2C1.
Finally, note that R2C2 can’t belong to R2C1, since otherwise, R3C2 must belong to R2C1 too to make the region R2C1 belongs to is a rectangle. But since R3C2 doesn’t belong to R2C1, then R2C2 can’t belong to R2C1 either. So R2C2 belongs to R1C2. Similar reasoning yields that R1C1 belongs to R2C1, and our puzzle is completed.