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Grouping setups

AR grouping setups

Grouping setups include assigning people to shifts or determining which activities a group of people choose to participate in.

The above setups are slightly different in that in the first scenario, people are placed in shifts, whereas in the second scenario, activities are assigned to people.

Order is of no significance in grouping scenarios. If both Pierre and Lina are in group A and group A has precisely two people, it doesn't matter who was first or second.

Grouping arrangements may sometimes feature the more straightforward 'in/out' rule, whereby either someone is in a group or not.

Click here for ordering setups.

Grouping setup examples

Order doesn't matter in groups. If A and B both belong in Group C, it doesn't matter if A comes before or after B.

Example 1:

Statement 1: There are four vehicles.

Statement 2: Two of the vehicles are blue.

Statement 3: One of the vehicles is a convertible.

If the first three statement are true then the convertible is blue.

True/False/Cannot be determined.


Example 2:

Statement 1: All dogs like to play.

Statement 2: Some dogs like to snow..

Statement 3: Some dogs like rain.

If the first three statements are true, which of the following statements must also be true?

1. All dogs who like snow like rain.

2. Dogs who like to snow also like to play.

3. Dogs who like to play do not like rain.

Statement 2 is correct.

Example 3:

Four friends visit a museum.

John and Mary are at the gift shop. Clive is looking at sculptures, and Pamela is looking at modern art.

If John switches places with Clive, and Clive then switches places with Pamela, where is Pamela?

Pamela is in the gift shop

Example 4:

Six friends, Abbie, Ben, Connie, Dave, Emily and Frank, are at the beach and are looking into how to pass the time.

Their decide on beach volley, swimming, and sunbathing.

Three more people are swimming that there are playing beach volley.

If Abbie, Ben and Connie are all sunbathing, then who is swimming?

Dave, Emily and Frank are swimming.


analytical reasoning diagram


Because of the rule that there are always three more people swimming than playing beach volley, there can only be two scenarios.

Given that three people are sunbathing, the rest can only be swimming, according to the first scenario.

Example 5:

A college debate society meets on Monday, Tuesday and Wednesday.

  • There are seven member in total, Anne, Barbara, Chrissie, Donald, Ethan, Frank, and George
  • There are three speeches on Monday, three on Tuesday and one on Wednesday, and each member will make one speech.
  • Rule 1: Anne's speech is on Monday
  • Rule 2: Chrissie and Donald have speeches on the same day
  • Rule 3: If Ethan's speech isn't on Monday, then Frank's speech isn't on Tuesday.
  • 1. Which college student will make a speech on Wednesday?



    analytical reasoning diagram


    analytical reasoning diagram


    The diagram illustrates the only correct scenario according to the rules.

    C and D, a pair according to rule 1, have Monday spots. Ethan cannot be on Monday, since there are no more available spots. According to rule 3 therefore, Frank is not on Tuesday. Frank is not on Monday either, because again, there are spots available. This leaves only one spot, Wednesday, for Frank to make his speech.

    The only other scenario places C and D, on Tuesday. In such a case, the Ethan Monday rule cannot come into effect, leaving no more information to place anyone in a spot.