Spiders are, as we know, square shapes with eight legs extending in pairs to the four sides. The legs come in two colors, and each color occurs four times. There are 20 different suborders (up to rotations), shown below. They are related to quadrons, to be discussed at a later time.
Today we will focus on balanced spiders that extend legs of different colors to each face. There are just six of them:
Spiders build spiderwebs by holding together along equally colored legs, as shown above. They prefer it if no two identical spiders occur in the same row, also as shown above. This single row of all six balanced spiders was easy.
The second row is a little harder, consisting again of all six different balanced spiders. We had to rotate some of them, they don’t mind that.
Adding more rows seems to be equally hard. Is this always possible? Then it should be possible to arrive at a 6×6 square of balanced spiders, each row a complete set of the six.
The dream of the spiders is to build a 6×6 spiderweb so that also all columns contain a complete set of balanced spiders. Please help them.
The Inner Frame 