# Circular Ordering

We have thoroughly studied the ordering of elements in a straight lineâ€”the most common type of LSAT game. In the next most common type of ordering game the elements are placed around a circleâ€”typically, people who are evenly spaced around a table. Circular diagrams have a few interesting properties not found in linear diagrams.

First, circular diagramsâ€”unlike linear diagramsâ€”are not fixed. That is, circular diagrams do not have a first, second, . . ., or last position. You can envision a circle as derived from a line by bending the line until the left end point (say, the first) and the right end point (say, the last) meetâ€”forcing the first and last elements to become one and the same. Hence, there is no beginning or end on a circle.

For this reason, you can initially place an element anywhere on the diagramâ€”it can be fixed only in relation to other elements. It is conventional to place the first element at the top of the circle. Then place any additional elements (where applicable) to the left of it, clockwise around the circle.*

Next, although there is no first, second, etc., on a circle, there is left-right orientation (at least locally). So if a condition states that one element is next to another element but does not state whether itâ€™s to the left or the right, then two diagrams that are mirror images of each other will be possible.

First, circular diagramsâ€”unlike linear diagramsâ€”are not fixed. That is, circular diagrams do not have a first, second, . . ., or last position. You can envision a circle as derived from a line by bending the line until the left end point (say, the first) and the right end point (say, the last) meetâ€”forcing the first and last elements to become one and the same. Hence, there is no beginning or end on a circle.

For this reason, you can initially place an element anywhere on the diagramâ€”it can be fixed only in relation to other elements. It is conventional to place the first element at the top of the circle. Then place any additional elements (where applicable) to the left of it, clockwise around the circle.*

Next, although there is no first, second, etc., on a circle, there is left-right orientation (at least locally). So if a condition states that one element is next to another element but does not state whether itâ€™s to the left or the right, then two diagrams that are mirror images of each other will be possible.

However, if there is no mention of the circleâ€™s orientation (left or right), then the mirror image of the diagram need not be considered. |

For example, if it is given that A is next to B, and it is not specified whether A is to the left or right of B, then only one of the following two possible diagrams need be considered. They will generate the same answer to any question.

**When you draw your circle, insert spokes.**Invariably, circular games involve an even number of people (usually 6 or 8) spaced

__evenly__around a circle. Therefore, a particular element will always be directly opposite another element. Drawing spokes inside the circle clarifies and highlights whether two elements are directly opposite each other, which often is a relevant issue.

Now that we have our circle drawn with spokes inserted, we come to

**the**

**decision**: which element(s) do we place on the diagram first.

Always place elements whose positions are fixed relative to one another first. |

Recall that with linear ordering games we first place any element whose position is fixed (first, second, last, etc.). Then we place any elements whose positions are fixed relative to one another (e.g., B comes after C). Circular diagrams, however, are not fixed. Hence, the first step does not apply, and we start with the second step.

The relative position of elements around a circle can be fixed in either of two major ways. First, two elements can be directly opposite each other. This forms a

**base axis**, which separates all the remaining elements to either side of it.

**Place the base**

**axis on your diagram first.**

Second, the elements can be immediately next to each other. This forms a

**base group**.

**Place the base group on your circle after you have placed the base**

**axis. Place it first if there is no base axis.**

Now letâ€™s apply these properties and strategies to a circular game of medium difficulty.