Setup and Rule Diagrams

[Dave Killoran]

This game is discussed in our Podcast: LSAT Podcast Episode 31: The September 2019 LSAT Logic Games Section

Setup and Rule Diagram Explanation

This is a Circular Sequencing game.

The game establishes that 7 artifacts will be in display cases, which are numbered and arranged in a circle. While this circular element is strongly stated in the scenario, the use of an odd number of items (and the corresponding loss of rules about artifacts being "opposite" of each other) and the fact that each position is numbered lead many test takers to show this as a Linear setup (all Circular games are linear, of course, so this is always an option, but even numbered games lend themselves better to the "spoke" diagrams typically used for Circular games). Consequently, the base setup is as follows:

• G H J M N P S 7
  
  
  
  ___ ___ ___ ___ ___ ___ ___
   1     2    3    4    5    6   7

Display cases 1 and 7 are still next to each, and that becomes an element to track throughout the game. With that in mind, let's examine the rules:


Rule #1: This rule establishes that H or J is in the seventh display case:

• ___ ___ ___ ___ ___ ___ _H/J_
   1     2    3    4    5    6   7

Rule #2 and #3: The second rule creates a sequence involving N and M, with N being to the left of M (remember: 1 is lower than 2, 2 is lower than 3, etc):

• N M

The third rule creates a rotating MH block, which can be added to the sequence created by the prior rule:

• N MH

Note that the block can be MH or HM, and on a diagram we'd show it with a circle around it to indicate that possible rotation.

This rule automatically creates limitations on where the variables can be placed, with N eliminated from the case 6, and H and M eliminated from the case 1.

Note also that this last inference allows us to deduce that if H is in the case 7, M must be in the case 6.


Rules #4 and #5: These two rules create three rotating not-blocks:

• PS PJ SJ

Because none of the three variables in these blocks can be placed next to each other, they require at a minimum 5 spaces to be separated (think of them in positions such as 1-3-5 at the minimum to avoid each other). The remaining variables—N, the MH block, and G (which is a random)—must then separate them. Understanding this J/P/S separation is one of the keys to the game!

So, for example, let's imagine a hypothetical in which H is in the case 7. In order to conform to the third rule we'll place M in the case 6 (note that, as discussed above, M can never be first so this will prove to be the only template possible with H in the case 7):

• ___ ___ ___ ___ ___ _M_ _H_
   1     2    3    4    5      6    7

The remaining variables are the trio of J, P, and S, with only G and N remain to separate them. Thus, J, P, and S would have to occupy display cases 1, 3, and 5, and G and N would have to occupy display cases 2 and 4:

• J/P/S G/N J/P/S N/G J/P/S _M_ _H_
   1          2         3         4         5        6         7

This if course represents just one solution pattern to the game, but it shows how powerful the J/P/S not-block arrangement can be, and the separation role that must be played by the other variables. Remember, if you suspect something is happening with the variables but you can't quite identify it, try a hypothetical or two!

[gwlsathelp]

Can you explain the limitations on the HM rotating block a bit more? I don't quite understand how M cannot be placed on the first spot.

[gwlsathelp]

Can you explain the limitations on the HM rotating block a bit more? I don't quite understand how M cannot be placed on the first spot.

For more clarification, there is not a rule that states that the mask must be a higher number case than the necklace and the helmet and mask just have to be next to each other.

[Dave Killoran]

For more clarification, there is not a rule that states that the mask must be a higher number case than the necklace...

There actually is, it's the second rule. This is why M cannot be first.

Regardless of that, anytime you see a Not Law or a discussion of a place a variable cannot go, if it doesn't make sense, put the variable in that spot and see what happens--there will always be a violation somewhere

Thanks!

[IguessIdontgetit]

I am confused by how H could not be in case 1. Case 1 and 7 are next to each other and there is no rule stating that N must be before H, just that is must be before M.

So why wouldn't a board like:

(H N P S G J M) be valid?

I must be missing something but I am not seeing it.

[IguessIdontgetit]

I am confused by how H could not be in case 1. Case 1 and 7 are next to each other and there is no rule stating that N must be before H, just that is must be before M.

So why wouldn't a board like:

(H N P S G J M) be valid?

I must be missing something but I am not seeing it.

Nevermind, I see it, I'm completely disregarding that H/J at 7 rule.