There are only so many ways to disguise a game. Whether a game discusses sequencing or grouping world class pogo stick champions, clowns, attorneys, houses, or whatever doing one thing or another, the underlying logic never changes. Furthermore, there are only so many ways to craft rules and only so many ways these rules can interact with each other to create inferences. While the LSAC has been getting substantially more creative, a large portion of games continues to rely on the same rules and inferences they have for the past three decades. **Logic Games Recurring Inferences** is devoted to these repeated inferences. Some of these may seem obvious or trivial, but the goal is to approach and understand these at an abstract level and build our way up.

#### Sequencing and Ordering Game Logic Games Recurring Inferences

- Follow/Be the leader: pushing a variable off the game board
- The mediator: splitting a not block with a third variable
- Sequencing Game Inference 2
- Sequencing Game Inference 3
- Sequencing Game Inference 4

## Grouping Logic Games Recurring Inferences

- Grouping Game Inference 1
- Grouping Game Inference 2
- Grouping Game Inference 3
- Grouping Game Inference 4

Follow/Be the leader; pushing a variable off the game board

This is the most common type of inference that often appears as a direct question. You can also use it to create not notations (where variables cannot go) on your global game board. The basic idea is some set condition – board size or position of other variables – restricts the location of some chain or block of variables.

Simulated Logic Game Language | Abstracted Logic Game Language |

There are five orchestral xylophonists – Alexander, Beatrice, Collin, Dean, and Ellie – that sit in chairs numbered one through five. |
Variables = Orchestral Xylophonists { A, B, C, D, E }Sounds like a sequencing game |

Alexander sits in a lowered number chair than Dean and in a higher numbered chair than Beatrice. | B – A – D |

Collin sits in the chair numbered exactly one lower than the chair Dean sits in. | CD |

Global game board:

B – A – CD

We can combine our first and second rule to get the above sequence. If CD are immediately adjacent, nothing can come between them, so B must precede A which must precede our CD block. From the above rules, we can make a whole slew of the Follow/Be the Leader inferences.

C/D | |||||||||

1 | 2 | 3 | 4 | 5 | |||||

We know that Beatrice has to be in a lower numbered chair than Alexander, Collin, and Dean, so Beatrice cannot sit in the third, fourth, or fifth chair as there would not be enough room for those that must sit in higher numbered chairs.

We know that Alexander has to sit in a higher numbered chair than Beatrice and a lower numbered chair than Collin and Dean, so Alexander cannot sit first, fourth, or fifth as there would not be enough room for either Beatrice, Collin, or Dean to sit.

We know that Collin must sit in a higher numbered chair than both Beatrice and Alexander, so Collin cannot sit in the first or second chair as there would not be enough room for Beatrice and Alice. Furthermore, Collin must sit in the chair one position lower than Dean, so Collin cannot sit in the fifth chair either.

We know that Dean has to be in a higher numbered chair than Beatrice, Alexander, and Collin, so Dean cannot sit in the first, second, or third chair as there would not be enough room for those that must sit in lower numbered chairs.

For examples of **Follower/Be the leader** in action, you can go to just about any sequencing game. For more involved and complicated inferences, I will list some examples of actual games that use them.

BONUS INFERENCE: How did we know that either Collin or Dean must sit in the fourth chair?

Let us think about this one. We have our Collin-Dean block. They can’t be separated. They like to hold hands during downtime from playing their xylophones in the orchestra. If we look at our not rules, we will see that Dean can only sit in the fourth or fifth chair. If Dean sits in the fourth chair, he’s there. If he doesn’t, he must sit in the fifth chair which means Collin must sit in the fourth chair; either way, Dean or Collin must sit in the fourth chair.

Alternatively, let us see why Eric cannot sit in the fourth chair! We already know that Beatrice and Alexander have too many people that sit in higher numbered chairs than them to sit in the fourth chair. Let’s sit Eric there and see what happens! I’ve ignored the not labels from above so we can really hone in on this. First, let’s try to put the Collin-Dean block after Eric in the fourth chair.

E | C | ||||||||

1 | 2 | 3 | 4 | 5 |

Whoops! Apparently, there is no room for Dean. Let’s try putting the Collin-Dean block before Eric in the fourth chair.

A | C | D | E | ? | |||||

1 | 2 | 3 | 4 | 5 |

Whoops! There is no place for Beatrice to sit, and our fifth chair is empty! This is a related inference that occurs in games, and we will discuss it again later. This is another important inference to learn!

**Filler text come up with another name for this to reference to**

The mediator: splitting a not block with a third variable

While not as common as the first inference we discussed, this concept comes up a lot in logic games. The basic idea is that some limited number of adjacent slots (typically three) must be filled by three variables. Two of these variables will be prevented by being next to each other due to a not block rule.

Simulated Logic Game Language | Abstracted Logic Game Language |

There are five famous world class pogo stick champions – Alice, Bradley, Christina, David, and Eric – that placed first through fifth in descending jump hieght order. |
Variables = World Class Pogo Stick Champions { A, B, C, D, E }Sounds like a sequencing game |

The world class pogo stick champion that jumped highest places first, and there were no ties in the grueling competition. | Definitely single layer sequencing and the highest jumper places first. |

Alice and Bradley did not place next to each other. | |

Christina pogo stick jumped the highest, won the competition, and came in first place. | C_{1} |

David pogo stick jumped the lowest and came in last place. | D_{5} |

Global game board:

C | D | ||||||||

1 | 2 | 3 | 4 | 5 |

We have three variables remaining (Alice, Bradley, and Eric) that must be placed in three adjacent slots (2, 3, and 4) with one rule that has not been applied, ‘Alice and Bradley placed did not place next to each other.’ If we ignore this rule, Eric could conceivably be placed in the second, third, or fourth position as seen in board a), b), and c) respectively.

a) | C | E | D | ||||||

1 | 2 | 3 | 4 | 5 |

Note: a) does not work, as it would force Alice and Bradley to place next to each other.

b) | C | A/B | E | B/A | D | ||||

1 | 2 | 3 | 4 | 5 |

Note: b) is the only option that works. Eric must be in the third position as it is the only way to separate the two variables that hate each other, Alice and Bradley, from violating the rule that separates them.

c) | C | E | D | ||||||

1 | 2 | 3 | 4 | 5 |

Note: c) does not work, as it would force Alice and Bradley to place next to each other.

This inference shows up a lot in logic games, and it will always be true regardless of whether the game is about thespians, clowns, attorneys, or whatever the LSAC feels like talking about. This inference, like the first one discussed, shows up frequently in both the initial game setup, as shown above, and with local conditions.

For examples of this inference in action, you can go to ________________________________list of logic games with this recurring inference, the mediator: splitting a not block with a third variable.

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