Click here to view or download a pdf file with the 1797 solutions on 30 pages.

Kwazy Quilt

How I solved the Kwazy Quilt puzzle

by Joel Gyllenskog

The Kwazy Quilt puzzle has 13 pieces. Each piece has from 1 to 6 points like the points of a snowflake. Finding all possible solutions to the puzzle is not that difficult with a computer to do the heavy lifting. An exhaustive state space search doesn’t take very long, but displaying the solutions is an interesting problem.

To display the solutions requires 63 different glyphs to show each piece in each possible orientation. For the sake of completeness glyph 64 is added which is a circle with no points on the edge. Often a complete solution is not much more work than just covering what we think we will need. Here are the pieces showing all possible orientations of each piece.

Eliminating duplicate solutions

Once a solution is found it can be viewed four different ways. These four views are really just one solution. Here is an example.

The two solutions on the left are the mirror image of the two solutions on the right. Similarly, the two solutions on the top line are the mirror image of the two solutions on the bottom line. Not only that, but if the four solutions are rotated by 180 degrees it looks the same as it did before it was rotated.

One way to produce output without duplicates is to produce all of the possible solutions and then remove the ones that are duplicates. The preferred method, however, is to not produce the duplicates in the first place. With the Kwazy Quilt puzzle we look at all of the possible pieces in all of the possible rotations. The one piece that we can use to address this issue is this one:

The 12 different orientations of this piece are shown in 3 rows. In each row the glyph in the second column is a horizontal mirror image of the glyph in the first column. The glyph in the third column is a vertical mirror image of the glyph in the second column. The glphy in the fourth column is a horizontal mirror image of the glyph in the third column. By limiting the ways that this piece can be used to a single choice in each of the 3 rows eliminates all of the duplicates that come from mirror images of the solution. In our document showing all of the possible solutions this piece always appears in one of the 3 orientations shown in the first column.

Note that in the puzzle there are two different parts with just one point. In finding all of the possible solutions we were careful to not produce any solutions that are the same except that those two identical pieces are interchanged. In versions of the puzzle that have colored pieces if these pieces have different colors the solutions can look different if the pieces are interchanged, but we are only concerned about the shapes, not the colors.

Click here to learn how to find a solution without using a computer.