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Circular Ordering

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

First, circular diagrams—unlike linear diagrams—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) meet—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 diagram—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 it’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 circle’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.
To see this more clearly, hold this page up to the light and look at Figure I from behind the page. A is now to the left of B. If you turn the page back, A is to the right of B. Clearly, during this process, the relationship between A and B (their relative position) did not change—only your perspective did. Thus Figure II is not fundamentally different from Figure I.

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.
For example, if A is directly opposite B, then A and B form a base axis as follows: 

Second, the elements can be immediately next to each other. This forms a base group.
For example, if B is immediately between A and C, then we have the following 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 let’s apply these properties and strategies to a circular game of medium difficulty.

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