Square Dance Combinations

Gero Teufert, 09/1999


If you want to work out a system to get from a given formation (i. e. a Box) to an adequate "Allemande Left, Promenade" or "RLG-Getout, Promenade" get out, it is helpful to know how many Combinations the dancers can be placed within that formation. Therefore our knowledge of FASR- and FASROO-States helps us.

When working with symmetric choreography only, we find the following number of possible combinations for a given formation:


6 Arrangements X 4 Sequences X 4 Relationships
4 Orientations X 2 Occupations
768 Dancer Position States


Sound much, doesn't it? Fortunately, like we already mentioned in the articles before, many of those are similar in technical manner, as long as we are worrying with standard choreography. In that case we find only one eighth of the number above mentioned, because in the given example of boxes there are eight boxes from which you could call an adequate Allemande Left. Those eight boxes only differ in the Orientation and the Occupation of the outer position with heads or sides. Those boxes are alike from a technical view, we call them "technically equivalent".

Since we are looking for an "Allemande Left, Promenade" get out, we need to look at combinations that are not technically equivalent only .


In any symmetric formation, there are 96 technically non equivalent ways the dancers could be scrambled....


6 Arrangements X 4 Sequences X 4 Relationships
96 Dancer Position States


Even that number can be shortened. If we assume that firstly most common get outs work from standard arrangements (boys on the left, girls on the right) and secondly each caller should be able to get the dancers from non standard to standard arrangement, we need to look at one given arrangement exclusively.


In any formation with known arrangement (e.g. standard arrangement Boxes), there are only 16 ways the dancers could be scrambled....


4 Sequences X 4 Relationships
16 Dancer Position States



last Update: 10.12.1999

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