LEGO + Geometry

Besides my fascination with LEGO bricks, I have many other hobbies and interests. One such pasttime has been crafting puzzles, games, and brainteasers of various sorts. Often I craft the necessary pieces out of wood, but other times I make use of whatever is available (local school supply shops love me because I'm always buying tokens, dice, letter tiles, marbles and the like).

It finally sunk in recently that for rectagular pieces that need to be fashioned with high precision, LEGO bricks would be a fine material with which to work.

My first 'LEGO puzzle' (I expect there to be many more) is a recreation of the classic Pentominoes Pieces Puzzle. A 'pentomino' is a geometric shape formed by the edge-to-edge joining of five unit squares. There are twelve such unique pieces (not including reflected images).

With twelve pieces at five squares each, this creates pieces which cover an area of sixty units (12 X 5 == 60). Thus, one challenge is to try to fit the pieces into a perfect rectangle of given dimensions; say, a 6 x 10 rectangle.

Much more can be discussed about the mathematical properties of pentominoes (see below for related links). The challenge I posed for myself was to build twelve such pentominoes out of LEGO bricks and plates and tiles, and a tray into which to place them.

Actually, this had already been done, so, in order to add a little newness to the project, I came up with an additional challenge. I would make the pieces and tray out of LEGO bricks and make each piece a different color.

That's thirteen colors total (one for each piece and one for the tray).

Whoa... I thought my Princess Mononoke model was a difficult experiment in rare colors, but this... this would require thriteen different LEGO colors.

At least the Pentomino Puzzle is a small item; if I could find enough colors, I wouldn't need too many.

With my challenge set I started hunting about Brickbay and BAYLIT to see if I could track down enough plates and tiles of each color.

Sure enough, I did... barely.

For the tray I chose Black. For the pieces I ended up using the following colors: Blue, Brown, Dark Gray, Gray, Green, Orange, Red, Sand Green, Tan, Teal, Yellow, and White.

A picture of the finished (and solved) puzzle is below (you may click on it to see a few more photographs).

For those of you who are as intrigued by Pentominoes as I am, you may be interested in set of miniature LEGO pentomino sets I sell.

And yes, there are multiple ways to solve this puzzle; and there are many other interesting configurations into which these twelve pieces may be placed. If such things interest you, I encourage you to investigate the links below:

Modulex Pentominoes

In early 2002 I constructed a second set of Pentominoes, this time out of 'miniature LEGO' bricks called Modulex bricks (for more information about Modulex bricks, refer to the webpage about my first project that used them). I had built the puzzle one day while in Los Angeles (I was there for the BricksWest 2002 convention).

A week later I was pleased to give the pentominoes to a promising new Scrabble player (I was in a Scrabble tournament then). Her future as a tournament Scrabble player is as bright as she is smart and adorable (congratulations on your first tourney wins, Elinor).

The picture below shows myself working with the puzzle pieces (photograph by Brian Haines). All of the pieces were constructed with clear Modulex bricks; the tray to hold them uses pink and lemon colors.


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