Object: Tile rectangles with squares (such that no two square tiles have a side in common).
(2 variants, over 1100 solutions!)

There are two ways to draw squares:
1. 'Speed Draw': Click the board to specify the position of the bottom right corner of a square only. The program will automatically draw the largest square possible that can be fitted.
2. '2-Point Draw': To place a square click the board for the top left corner, then for the bottom right corner.
You can switch between the two modes at any time. The largest available tile is a square of size 30x30.

You can hit the FRAME button and then click the main board to draw a frame for a rectangle to be filled.
Hit the one of the four ARROW buttons to shift the whole tiling.

DEFAULT VARIANT:
The goal is to completely tile a large square or rectangular area with smaller squares such that no two tiles may not have a side in common ('nowhere-neat tiling').
The following sizes of non-square rectangles smaller than 50x50 have been solved under this condition:
11x15, 12x(18,33,48), 13x(40,43,46,50), 15x(17,24,31,33,39-40,42,45-47,49-50), 16x(18,28-29,32-50), 17x(27,30-32,34-50), 18x(23-27,29-50), 19x(21,25-50), 20x(22-24,26-50), 21x(23,26-50), 22x(23-50), 23x(24,26-50), 24x(25-50), 25x(26-50), 26x(27-50), 27x(28-50), 28x(29-50), 29x(30-50), 30x(31-50), 31x(32-50), 32x(33-50), 33x(34-50), 34x(35-50), 35x(36-50), 36x(37-50), 37x(38-50), 38x(39-50), 39x(40-50), 40x(41-50), 41x(42-50), 42x(43-50), 43x(44-50), 44x(45-50), 45x(46-50), 46x(47-50), 47x(48-50), 48x(49-50), 49x50.
All other rectangles (<50x50) do NOT have a fault-free solution.
All known solutions (over 1000) have been added.
Rectangles which only have a tiling with a fault line (such as 11x22) are not listed here.

The system will add 1x1 squares automatically if an empty position has three occupied neighbors!
If you do not want this, click the 'Autofill 1x1' button to switch it off.
To delete an existing square click it anywhere.

A special solution display tool has been added (click the SOLUTIONS button or view a subset of solutions by clicking one of the buttons at the bottom border).
If possible, solutions should be fault-free (no breaking line) and should not be enlargements of other solutions.

FREEPLAY VARIANT:
Here are no restrictions; two squares may have a side in common.

There is no win-message in this game.

Please note that there are 25 alternative board/piece set combinations available (hit 'change piece sets' button).
The default piece set shows the size of each square tile at its lower left and right corners.

Nearly all solutions have been found by hand by the author. A few cases have been solved by the game 'Square The Square Solver' ('STS-Solver').
For all sizes 50x50 or smaller it is now known whether there is a nowhere-neat solution or not.
There are still a lot of additional solutions to be found. So give it a go; you might discover some new tilings yourself!

The idea for these puzzles is taken from my books 'NUTTS And Other Crackers' and 'New Mosaics' (see my home pages).
The special property of the tilings of no two tiles having a side in common is called 'nowhere-neat'. The author Karl Scherer showed in 2005 that there is a solution for each R(n, m) with n > 1187 and m > 464. The mathematical proof for this theorem is attached.

There is also a corresponding threorem by the author regarding the no-touch and nowhere-neat tilings of squares with smaller squares. For details see the Zillions games 'Square The Square' and 'Square The Square II'.

Related Zillions games: 'Square The Square', 'Square The Square II', 'Square The Square Solver'.