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Diagramming Continued

As stated before, diagramming is the way to solve nearly every game. This section covers how to construct an efficient and functional diagram. The process is very mechanical.
 
We begin with the setup to a game. The setup gives the context or background for a game. The elements, often people, are named here, too. We abbreviate names by using the first letter of the name. Kindly, the LSAT writers use names that begin with different letters.
 
For example, we may be told that six people—Jack, Kathy, Larry, Mary, Nick, and Olivia—are seated, evenly spaced, around a circular table. We let J, K, L, M, N, and O stand for their names.
 
Next, take the conditions and turn them into symbols.
 
For example, suppose for the above setup we are told that
Jack sits at the “top” of the table.
Jack sits directly opposite Larry.
Mary does not sit next to Larry.
 
The first condition, “Jack sits at the ‘top’ of the table,” is naturally described as J = top. The second condition, “Jack sits directly opposite Larry,” can be symbolized as J<—>L (where the arrow means “sits directly opposite”). Finally, the third condition, “Mary does not sit next to Larry,” can be written as M ≠ L. [Another possible symbol is ~(ML). You may prefer to use this symbol or to create one of your own. The symbol you choose is irrelevant so long as it is short and functional.]
 
Adding these symbol statements to our previous work yields the following schematic:
 
J K L M N O
J = top
J<—>L
M ≠ L
 
Note, the elements O, K, and N are “independent” because no conditions refer directly to them. In general, independent elements can be placed in more positions on a diagram than dependent elements. Think of independent elements as “wild cards”.

Now, we need a diagram to complete our scheme. To this end, draw a circle with three spokes inside, and place it below the schematic:
J K L M N O (K, N, O are “wild”)
J = top
J<—>L
M ≠ L

 

Next, we come to the all-important decision—in what order do we place the conditions on the diagram.
 
The following rules should guide your decision.
  1. First, place conditions which fix the position of an element.
    Examples:
    Allison is second from the left.
    Steve works on Monday only.
  2. Next, place conditions which limit the positions an element may have.
    Examples:
    Allison is either the second or third person from the left.
    Steve works only the night shift.
  3. Then, place conditions which connect two or more elements.
    Examples:
    Allison sits directly opposite Jane.
    Steve works only when Bob works.
  4. Finally, on the diagram designate any place an element cannot be.
    (This is the negative counterpart of rule 2, and it is much weaker.)
    Examples:
    Allison cannot sit in an even numbered chair.
    Steve does not work when Bob works.
Diagramming Continued
Now let’s apply these rules to the conditions of our game. J = top is the only condition that fixes the position of an element, so place it on the diagram first:

 
Next, scan the conditions for one that limits the placement of an element. There are none. So, the second rule does not apply.

Then, scan the conditions for one that connects two or more elements. The condition J<—>L connects J and L. Place it on the diagram as follows:

 
Finally, scan the conditions for one that tells where an element can not be. The last condition, M ≠ L states that M cannot be next to L. Thus, our final diagram looks like this:
J K L M N O (K, N, O “wild”)
J = top
J<—>L
M ≠ L

 

This diagram is self-contained. There is no need to refer to the original problem. Looking back should be avoided whenever possible.

Short Drill on Order of Placement

 

Directions:  Using the guidelines on this page, determine the order in which each of the following sets of conditions should be placed on a diagram.
 

Questions

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