Pentominception

It’s been a while since I last wrote an article about a STEM topic.
Recently, I reconnected with my childhood by creating a design based on a puzzle I had when I was a kid. It all started when my dad bought a 3D printer a few months back and he decided to print the puzzle.

As I was conducting some research, I made an accidental discovery which blew my socks off. That led me to create a design using the Canva app which I am currently using to create visuals for my Instagram.

Here is what the puzzle looks like.

It is an 8×8 square tile puzzle with 13 pieces. 12 of them consists of an area of 5 squares while the middle square piece an area of 4 squares. If you do the math,
(12 * 5) + (1 * 4) = 64, it checks out perfectly.

Here is what it looks like with the grid lines for the tiles

Back then, there wasn’t any Google, so I had no idea what the puzzle is called or how many solutions are possible. Using brute force alone, it took me multiple attempts to obtain a few solutions. Not bad for a ten year old!

If you do a quick google search for ‘Pentominoes,’ you will find an exhaustive list of information & its history.

There are 2 variations of the puzzle. The square piece could either be fixed in the center or at random.

Here comes the discovery which left me speechless.

If the square piece was placed the middle, there will be 260 solutions.
Since a square has an order of symmetry of four(see appendix for explanation)
there will be 260/4= 65 unique solutions.
There are 64 square tiles in a large square.
Each solution can be placed on a tile.
The final solution will then be placed on the large 8×8 square.

My next task is to pick a set of 13 colours which will complement the design aesthetically.

While doing a quick research on colours, I stumbled upon another revelation about how the hex code is used to represent the shades of colours, which I will share in a separate post.

After reading this far, I hope that explains why the title of this post is ‘Pentominception’ = Pentomino + Inception

Without further ado, here is the moment you’ve been waiting for.

**Another victorious collaboration between math and art!**

The solution which is on the large square is the one that was etched into my memory when I was ten.

I don’t know about you, but my senses were tingling after seeing the final design. If you felt inspired by this post, be sure to pass it on. Get in touch with me if you’d like to get your hands on the pentomino puzzle set. Cheers!

APPENDIX

A square has order of symmetry is 4. In other words, you could rotate a square by an angle of 90 degrees and it will have the same orientation as before. The four squares below consists of the same unique solution. Just observe the position of the 4 red dots.