# Pattern Schemes (and some lovely Maths)

Tillions come in five types. Those which join on four sides (middles), three sides (borders), two adjacent sides (corners), two opposite sides (runners) and one side (finials). In these diagrams, each little square represents a tillion and you will see that they have bold lines on 1,2,3 or 4 sides. The bold lines represent the joining sides. The different colours represent different patterns, so if there are four yellow “middles” and eight blue “middles” in a diagram it just means that you will need four of one design and eight of another. At the bottom of each card is a list of what you need to make that pattern. This can be used as a challenge, keeping the diagram covered, perhaps with a hint such as“make a five by five square”and using the tillions in the recipe the player tries to make a "true" pattern (ie one where every joining side joins). Each diagram can be used to make hundreds of different patterns. All these patterns are symmetrical, but of course you can make anything you like.  ## The Calculation of Options

The number of different ways each pattern can be made using a large box of Tillions is shown on these cards. This calculation is made by multiplying the number of available designs for each element of the design. So in the first pattern shown here there are six corners to choose from, then seven borders to choose from, then (as one has been used) six borders left to choose from, then eighteen middles, then seventeen. When all multiplied together there are 77,112 different ways this first pattern can be made. All of them will be pleasing.     