MiniMatch-I:  variations and other figures

Here are some additional color themes to solve by matching the 9 MiniMatch-I tiles. A few have amazing symmetries (reflection), as well as wrap-around edges (opposite borders match) and enclosed colors. You are welcome to print out this page to add to your MiniMatch-I booklet.
Sample solutions with no enclosed color, no matching opposite borders:

Sample solutions with one enclosed color, no matching opposite borders:

Moebius solutions, where opposite sides match but with a half twist. The solution on the right is a double Moebius, which makes it into a "projective plane" if it were wrapped across both ways.

Sample solutions with double wrap-around edges and enclosed colors. The last solution also has a perfect symmetry of all colors:

There are 12 enclosed squares in any 3x3 MiniMatch-I matched solution. These can be filled by 3 or 4 colors in almost any combination. This research was inspired by Eric Bare's question whether the 4-4-2-2 division could be achieved with any combination of the four colors contributing the two groups of 4, and indeed the answer is yes to all 6 possibilities. Here are all the possible divisions of the four colors among 12 squares. Only 5-5-2 and 5-5-1-1 are not solvable because there are not enough tiles of the two minority colors to complete the border.

Shapes made of 9 squares evenly joined on their edges are also known as enneominoes. The ones we show here are just a few of the dizzying total of 1285 different shapes. All of those can also serve as a MiniMatch-I color-matching challenge, if you'd like to tackle them. The hardest ones are, of course, the "chunky" shapes that have the most contact edges.

Going wild...

If any one of the 3x3 solutions were regarded as a unit tile, say for covering a floor or wall with mosaics, there is no end to the patterns and variations you can achieve. Here are a couple of assemblies of just 49 of a single unit formed into 5x5 panels. Thanks, Joe Marasco, for suggesting this expansion idea.


What an incredible change just the tiniest adjustment can make. Imagine, then, what diversity the slightest mutations of DNA can produce. And we're using just 4 colors here; imagine if 6 or more were added. When does artistic order like these become a nightmare of chaos?

Here is another expanded replication of a single tile, by Patric Hale, who suggests this plaid should become our tartan (left). Because Patric likes a bit of chaos in his Universe, he added a little twist as perhaps a doorway into the mystery (right):


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