Click the board to mark the size of the square or rectangle you want to fill. The program will paint a horizontal and vertical wall.
The rectangle will be positioned at the top left corner of the large board. Its maximum size is 50x50.
The maximum size of a square tile the system will use to fill the area is 30x30.

The program will automatically start and search for a solution. It will try to fill the rectangle with squares in such a way that no two squares have a full side in common (nowhere-neat condition).
Some 'intelligence' has been built in to make the search more efficient. (E.g., when filling the 15x15 rectangle the program does not make a single mistake!)

If there is a solution, the system will find one (there may be more than one solution).
If there is no solution, the system will tell you that you have lost the game.
Squares with known solutions: n= 11,16,20 and all n>21.
Rectangles with known solutions (1 =< a,b =< 50) : see game 'Square The Rectangle'.

SPAN option:
As default, a tile may not span the whole width of the rectangle. If you want to allow spanning tiles, delete the NO SPAN text at the right border (use DEL key and mouse click).
Note that SPAN option is ignored (SPAN is disallowed) if NO FAULT LINES option is chosen; see below. FAULT LINES option:
As default, fault lines (also called 'braking line') are avoided, hence there will be no line running through the tiling from one side to the other. This can speed up the search dramatically.
A rectangular tiling with a fault line consists of two smaller rectangular tilings.
If you want to allow fault lines, delete the NO FAULT LINES text at the right border (use DEL key and mouse click).
Note that the NO FAULT LINES option implies NO SPAN.

Variant 2: Program tries to find all solutions.
Once the program has found a solution, it does not stop, but goes on searching for the next solution.
The number of solutions found are indicated by yellow dots at the upper left border.
You can see the tilings by checking when the red dots have been created (use the movelist).

Variant 3: Program tries to find all solutions.
Once the program has found a solution, it does not stop, but goes on searching for the next solution.
The number of solutions found are indicated by yellow dots at the upper left border. You can see the tilings by checking when the red dots have been created (use the movelist).

Variant 4:
Like variant 3, but human defines first square (at top left corner).

Variants 5 to 8: NO-TOUCH TILINGS
Like variant 1 to 4, but here the tilings are NO-TOUCH tilings, which means that square tiles of the same size may not have any length of boundary in common (they may touch at corners, though).
Note that a no-touch tiling is always a nowhere-neat tiling.

Please note there are three alternative boards (piece sets) available.

The idea for these puzzles is taken from my books 'NUTTS And Other Crackers' and 'New Mosaics' (see my home pages), where I introduced the 'nowhere-neat' concept.
The solutions of type 'Square The Square' and 'Square The Rectangle' can be found in the Zillions games 'Square The Square' and 'Square The Square II'.

Two mathematical theorems which I found connected with this subject have been published in the Journal Of Recreational Mathematics, Vol. 32(1) 1-13, 2003-2004. One of the results states that there exists a no-where neat tiling for all squares of size 11, 16, 18, 19, 20, or greater than 21.