# Hybrid Games

In the ordering games we have studied so far, only one element at a time could occupy a particular position. However, in many ordering games two or more elements can occupy the same position at the same time. These games order elements as groups, rather than as individuals. (Grouping games will be presented later.) As you would expect, this added complication makes hybrid games harder than line-up games. Hybrid games are presented here because their ordering nature is more significant than their grouping nature. Some typical setups to these games are

- Seven books are placed on five shelves.
- A four-story apartment building has four apartments, one on each floor, and seven tenants.
- There are two lines of couples waiting to buy tickets to a play.

When analyzing hybrid games, pay close attention to the number of positions versus the number of elements. Also, pay close attention to the maximum or minimum number of elements that can occupy a particular position.

# Hybrid Game

A cupboard has five shelves numbered 1 through 5, from bottom to top; each shelf has two compartments. There are eight items—A, B, C, D, E, F, G, H—in the cupboard, no two of which are in the same compartment.

Items D and E are on the same shelf.

B is on the shelf directly below G.

If a shelf contains only one item, it cannot be directly above or directly below another shelf that contains only one item.

C is the only item on one of the shelves.

There is only one item on the fourth shelf.

As in the previous examples, we construct a diagram to help answer the questions. The condition

*“D and E are on the same shelf”*is naturally symbolized as**Δ=Ε**. The condition*“B is on a shelf directly below G”*can be symbolized as**G/B**. The condition*“C is the only item on one of the shelves”*can be symbolized as**C = alone**. The condition*“There is only one item on the fourth shelf”*can be symbolized as**4th = alone**. Finally, the condition*“If a shelf contains only one item, it cannot be directly above or directly below another shelf that contains only one item”*can be symbolized**not 1/1**. This yields the following diagram:**D = E**

**G/B**

**C = alone**

**4th = alone**

**not 1/1**

****

Two readily derived conditions should be noted: There are 10 compartments, 8 items, and C is the only item on its shelf. So two shelves must have only one item each, and no shelf can be empty. Neither of these conditions can be placed on the diagram, so we turn to the questions.

Example-1

If H is on the fourth shelf, which one of the following CANNOT be true?

- A is on the second shelf.
- D and E are on the second shelf.
- D and E are on the top shelf.
- C is on the first shelf.
- A is on the third shelf.

Solution

Add the new condition, “H is on the fourth shelf,” to the diagram:

Now we attack the answer-choices, attempting to construct a diagram for each one. The answer-choice for which a valid diagram cannot be constructed will be the answer. Start with choice (A). Place A on the second shelf:

Next, place the condition

Then, place

Finally, place C on the bottom shelf and F on the third shelf:

This diagram does not violate any initial condition. Hence, A
Next, attack choice (B). Place the condition

Clearly this diagram leaves no room to place the condition
As we work through the remaining questions, note the determining power of the condition of

Now we attack the answer-choices, attempting to construct a diagram for each one. The answer-choice for which a valid diagram cannot be constructed will be the answer. Start with choice (A). Place A on the second shelf:

Next, place the condition

**G/B**on shelves 2 and 3:Then, place

**D = E**on the top shelf:Finally, place C on the bottom shelf and F on the third shelf:

This diagram does not violate any initial condition. Hence, A

*can*be on the second shelf. This eliminates choice (A).**D = E**on the second shelf as follows:Clearly this diagram leaves no room to place the condition

**G/B**. Hence, the answer is (B).**G/B.**Example-2

Which one of the following is a complete and accurate list of the items any one of which could be on the top shelf?

- D
- D, E, G, C
- D, E, G, B
- D, E, G, C, F
- D, E, G, H, F, A

Solution

The first thing to note about the answer-choices is that they all contain D. So there is no need to check whether D can be on the top—it can.
Next, since D and E must be on the same shelf, we eliminate (A).
Next, since all remaining choices contain G, there is no need to check whether G can be on the top shelf.
Next, since G must be above B, B clearly cannot be on the top shelf. This eliminates choice (C).
Finally, C cannot be on the top shelf; if it were, then one shelf with only one item would be directly above another shelf with only one item.
This eliminates both (B) and (D). Hence, by process of elimination, the answer is (E).

Example-3

Which one of the following must be true?

- If A is on the third shelf, then E is not on the top shelf.
- If E is on the second shelf, then C is not on the bottom shelf.
- If H is on the fourth shelf, then D and E are not on the second shelf.
- If B is on the fourth shelf, then D is not on the third shelf.
- If G is on the top shelf, then H is not on the bottom shelf.

Solution

This question is long because it actually contains five distinct questions. During the test you should save such a question for last. However, there is a shortcut to this particular question.
Notice that answer-choice (C) merely rewords Question 1 and its answer. Hence, the answer is (C).

**Note:**It is not uncommon for the LSAT writers to repeat a question with a different form. Being alert to this can save time.

Example-4

If G is on the top shelf and A is on the third shelf, then which one of the following must be true?

- D is on the first shelf.
- E is on the second shelf.
- C is on the fourth shelf.
- Either F or H must be on the same shelf as A.
- F is on the same shelf as G.

Solution

Add the new conditions to the diagram:

Next, add the condition

Now the condition

Next, since C must be alone, it must be on the second shelf in Diagram 1 and on the bottom shelf in Diagram 2:

Clearly in both diagrams, either F or H must be next A.
Hence, the answer is (D).

Next, add the condition

**G/B**to the diagram:Now the condition

**D = E**can be placed on either the first or second shelf. We construct a separate diagram for each case:Diagram 1 | Diagram 2 |

Diagram 1 | Diagram 2 |

Example-5

If A and B are on the second shelf, which one of the following must be true?

- D and E are on the top shelf.
- F is on the same shelf as H.
- A is directly above F.
- C is on the fourth shelf.
- C is on the first shelf.

Solution

Adding the new condition to the diagram yields

Next, adding the condition

There are two places left for the condition

In Diagram 1, the condition
Hence, the answer is (A).

Next, adding the condition

**G/B**to the diagram givesThere are two places left for the condition

**D = E,**the bottom shelf or the top shelf. We construct a separate diagram for each case.Diagram 1 | Diagram 2 |

**C = alone**must be placed either on the top shelf or the fourth shelf. But in either case this violates the condition that a shelf with only one item cannot be either directly above or directly below another shelf with only one item. This eliminates Diagram 1. In Diagram 2, D and E are on the top shelf.# Points to Remember

- Hybrid games order elements as groups, rather than as individuals.
- When analyzing a hybrid game, pay close attention to the number of positions versus the number of elements. Also pay close attention to the maximum or minimum number of elements that can occupy a particular position.
- It is not uncommon for the LSAT writers to repeat a question in a different form. You can save time by watching out for this.