A game of patterns, published by Kadon
By Scott Kim

AVAILABILITY. A beautiful acrylic version with raised black squares is published by Kadon. For a free version you can print and cut out, click here.

INSPIRATION. I have always been fond of games like Hex and Bridg-It in which the goal is to create a continuous path. My biggest influence was a path game involving hexagonal tiles called Psychepaths, by Charles Titus and Craige Schensted, now reincarnated as Kaliko (also published by Kadon). Since square and hexagonal path tiles had already been tried, I decided to do something different.

STORY. My 9th grade geometry teacher Walfred Lester asked his students to give reports on subjects of their own choosing. I decided to make up a new game, which I called Quintapaths.
     Each of the Quintapath sticks is a different sequence of 5 squares, each of which may be black or white. Sticks that are mirror images of each other are not counted as different, so there are only 20 sticks, not 32.
     The original challenge was to arrange the pieces in various patterns so the black squares make one continuous path:
     1. Arrange all the pieces side by side in a 5 by 20 rectangle so the black squares a single continuous path. The path may touch itself at corners, but may not contain 3-way junctions or 2 by 2 blocks, as shown here:

     Figure 1a at right shows one solution. Note that pieces 1 and 20 must always be placed at the ends. Can you complete pattern 1b? Is it possible to make a continuous path using pattern 1c?
     2. Try making a continuous path of black squares with the pieces arranged in a 10 by 10 square, as shown in figures 2a, 2b, 2c and 2d. Again, no branching or 2 by 2 blocks are allowed. Harder question: using any of these arrangements, can make a continuous path that joins itself in a loop?
     3. Can you arrange all twenty sticks in four 5 by 5 squares, as shown in figure 3, so squares 1 and 2 have the same pattern of black and white squares, as do squares 3 and 4?

     In 1997 I showed Quintapaths to Kate Jones, head of Kadon. She loved it. Before she could publish it, she set to work inventing dozens of new puzzles and games to play with the Quintapath pieces. Master puzzle designer Anneke Treep also joined in the lively email brainstorm. The results are published in the booklet that accompanies the Kadon version of Quintapaths.
     One of Kate's favorite questions is Yin Yang: create a 10x10 design in which there is just one connected mass of black squares, and one connected mass of white squares, both exactly the same shape. One shape will be an exact 180 degree rotation of the other. See the Kadon web site for the answer.



Copyright 2000 Scott Kim.
All rights reserved.