# Rectangles formed from every tetromino, tromino and domino

Can you form a 4x7 rectangle from every tetromino, tromino and domino? There are 5 different tetrominoes, 2 trominoes and 1 domino. Can you find different arrangements that are not mirrors/rotations of each other?

Bonus question: can you also form a 2x14 rectangle with the same shapes?

Good luck!

## 4 Answers

For completeness, all the solutions, excluding rotations and reflections.

1522 for the 4x7 and 84 for the 2x14.

Simlar to Dr Xorile, I think there are many solutions. Here are several:

The first one here is my first attempt, it was quite easy. The others are just mutations of it.


_____________
|  ___|_____| |
|_|_  |_   _|_|
|   |___|_|_  |
|___|_______|_|
_____________
|  ___|_____| |
|_|_   _|  _|_|
|   |_|___|_  |
|___|_______|_|
_____________
|  ___|_______|
|_|_  |_   _| |
|   |___|_| |_|
|___|_____|___|
_____________
|  ___|_____| |
|_|_  |_   _|_|
|  _|___|_|   |
|_|_______|___|
_____________
| |_____|___  |
|_|_  |_   _|_|
|   |___|_|_  |
|___|_______|_|

• +1 for the asci art! That's cool! – Dr Xorile Oct 16 '19 at 0:51
• @DrXorile Thanks! – Matthew Jensen Oct 16 '19 at 21:58

Here's 2 fundamentally different solutions:

I suspect there are many because these are literally the first two things I tried as I was playing around and in both cases I was able to just shove the pieces in and get a solution. I did it in the numerical order shown.

And here are a few 2x14 solutions:


11222444556778
11333345566888

11133344566788
12222445557788

11222444467788
11233355666778