A family member threw out a challenge for an education project she needed to deliver. Her idea was to create a puzzle using wooden Tetris blocks. Needing an excuse to spend more time in the garage, I set about figuring if it was possible to arrange Tetris blocks to create a completely filled rectangle. I resorted to trial and error using a 2D drawing in a 8x10 inch frame.  A number of combinations I tried resulted in 3 open squares, so I created a new puzzle piece to fill the space. Other than this anomalous block type, the rest of the blocks are all true to the Tetris shapes. I did subsequently discover that this is a well known math problem with well known solutions.... you can read all about it here http://en.wikipedia.org/wiki/Tetromino - you can select your frame size to to fit a known set of tetrominos. Had I spent more time on google I could have cut down on the trial and error! 

The Tetris objects are geometric shapes consisting of 4 squares with sides connected to each other on a square grid. The shapes are called Tetrominos and were made popular by the creator of  the Tetris video game Alexey Pajitnov in 1984 - thank you Wikipedia..... it's time to get specific about the puzzle.

There are many ways to physically make this puzzle. You can cut the shapes out of cardboard with a pair of scissors, use a scroll saw/jig saw/fret saw to cut the tetrominos out of wood, use a 3D printer to make them out of plastic or titanium (just kidding - while 3D titanium printing is available, I expect this would be a costly option) or use a laser cutter to make the shapes out of any suitable material including stainless steel. There are many possible solutions to the puzzle which provides hours of enjoyment. Some solutions are shown in the image gallery.

I used a CNC router to cut the terominos out of 1/4" plywood. The original process was to create the shapes in Visio, export the Visio drawing as a DXF, import the DXF into CamBam, generate the tool paths for the CNC Router and use Mach3 to control the cutting of the tetrominos from a sheet of roughly 14"x14x1/4" plywood. I lost the original raw data files and access to Visio, so this Instructable is a recreation and an excuse to familiarize myself with the 123D Design tool. You do not need 3D design tools for this - a simple pencil sketch on a 1" grid will suffice. But 123D is free  - free is good and 3D modelling is fun.

Step 1: 2D Trial

The first step is to create a set of tetrominos and arrange them to fill the proposed frame. I wanted the frame to be about 8x10 so I created the internal grid to be 7x9 to allow for a 1/2" border to contain the puzzle. The fact that 9x7=63 which is not divisible by 4 was completely lost on me at the time, which is why I ended up with a "3-block tetromino" for my last piece. If you adjust your frame size, you will be able to get everything to fit using standard 4-block shapes. I added an image and file that shows an 8x8 grid using only standard Tetris shapes that you can use as a basis instead.

I used OpenOffice Draw to create the 2D model. Unfortunately the app does not export a file format that the CAM software I used understands, so I recreated the 2D model in 123D. 

The OpenOffice draw file is attached - NOTE: Remove the PDF extension from the file. The file you want is TetrisPlan.ODG. Instructables appears to limit uploads according to file extension.

So Cool!
This looks fantastic! Can't wait to try it out. www.TetrisOnlineForFree.com
I've always liked these kind of puzzles. Nice.
add four legs and you have yourself a Tetris table :)
That's a good idea. A coffee table with Tetris top with a ton of tetrominos should keep the kids busy for a long time
How fun! I love puzzles!

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