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Seating Arrangement Questions and Answers

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Question 09 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 08 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 07 - Bancrofts School 11 Plus Maths Sample Entrance Paper 2023

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Question 01 - The Manchester Grammar School 11 Plus Entrance Examination Arithmetic Paper 2 2007

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Permutation and Combinations, Seating Arrangement

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Logical Problems and Seating arrangement

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Logical Problems, Even numbers, Seating arrangement and Addition

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seating arrangement

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Logic behind Seating Arrangement Questions for 11 Plus Exams

1. Seating Arrangement: Introduction

The seating arrangement is one of the most common question types, not only in 11 Plus exams but for various other competitive exams. In these questions, a group of people or objects are logically arranged following certain conditions mentioned in the problem. The arrangements are classified into the following four types.

1.1 Types of Arrangement

a) Linear arrangement:

  • People or objects are placed in a proper straight line.
  • The arrangement can be horizontal, vertical or diagonal.

b) Double row arrangement:

  • These arrangements involve two groups of people, with two parallel linear rows.
  • The persons in the two rows may face the same direction or may face opposite or different directions.

c) Circular arrangement:

  • People or objects are arranged around a circle or circular table.
  • People arranged around a circle are either facing the centre or facing the direction opposite to the centre.

d) Rectangular arrangement:

  • People or objects are arranged around a rectangle or rectangular table.
  • People arranged around a rectangle are usually facing towards the centre.

2. Tips and tricks to solve seating arrangement problems

For linear or double row arrangement problems:

  • Focus on the given information regarding the position of the person.
  • If it is given that A is sitting next to B, it implies that A and B are sitting together, with B either to the left or right of A.
  • If it is given that A is sitting left to B, it does not imply that A is immediately sitting left to B. There might be some other people sitting in between A and B.

For circular or rectangular arrangement problems:

  • Look out if the people are facing towards the centre or away from the centre.
  • If people are looking towards the centre, the right-hand side will be in the anticlockwise direction, and the left-hand side will be in the clockwise direction.

Seating Arrangement-11+ Topicwise Article-image 01

  • If people are looking away from the centre, the right-hand side will be in the clockwise direction, and the left-hand side will be in the anticlockwise direction.

Seating Arrangement-11+ Topicwise Article-image 02

2.1 Solved examples on seating arrangement

a) There are three people A, B and C and two chairs. In how many ways can these three people occupy the two chairs?

Solution:

Let the boxes below represent two chairs.

Seating Arrangement-11+ Topicwise Article-image 03

List all the possibilities.

Seating Arrangement-11+ Topicwise Article-image 04

The total number of possibilities = 6

This is the case of permutation as the position of people (A, B and C) is important here.

b) A round table has six seats placed around it.

Six children Anna (A), Drew (D), Jimmy (J), Noah (N), Pam (P) and Ruby (R) sit at the table.

Jimmy sits down as shown in the diagram.

Drew does not sit next to him.

Noah has Drew sitting next to him on his left.

Anna sits opposite Drew.

Pam sits next to Jimmy.

On the diagram, show where the children sit down.

Seating Arrangement-11+ Topicwise Article-image 05

Solution:

Drew cannot sit next to Jimmy, so he can sit in seats marked 1, 2 and 3.

Seating Arrangement-11+ Topicwise Article-image 06

Anna sits opposite Drew, so Drew cannot sit in the place marked 2.

1 and 3 are the two possible seats for Drew.

Noah has Drew sitting on his left, while Anna sits opposite to Drew.

So the possible seating arrangements can be:

Seating Arrangement-11+ Topicwise Article-image 07

Pam sits next to Jimmy, but according to the second possibility above, there is no space left for Pam to sit next to Jimmy.

So the first possibility is correct, and the final seating arrangement is:

Seating Arrangement-11+ Topicwise Article-image 08

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