This page covers Agniveer Army CEE Circular Seating Arrangement with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead this first — the foundation of the topic
Core Concept
In circular seating, positions are relative to each other. There is no first or last position. The key is to fix one person's position first, then arrange others relative to that person
Key Rules
1) Always fix one person's position to eliminate rotational possibilities 2) Clockwise and anti-clockwise directions matter 3) 'Opposite' means diametrically across 4) Adjacent means immediate left or right 5) Use process of elimination systematically.
Formula BlockMemorise — at least one formula appears in every paper
Total circular arrangements of n people = (n-1)! This is because we fix one position to avoid counting rotations as different arrangements. For restrictions like couples sitting together, treat them as single units.
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks 3-5 questions per set. Common question types include: immediate neighbors, opposite positions, counting positions between people, and conditional arrangements. Most questions give 6-8 people with 4-6 conditions.
ShortcutsUse these to save 30–60 seconds per question
1 - The Fixed Position Method: Always start by placing one person at the 'top' of the circle. This eliminates confusion about rotational arrangements. Mark positions as 1,2,3... clockwise from this fixed person.
Shortcut Trick 2 - The Opposite Formula: In a circle of n people, if person A is at position x, then the person opposite to A is at position x + n/2 (if n is even).
For odd numbers, no one sits exactly opposite.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Fix A at position 1 (top)
2
Step 2
B sits two places right of A, so B at position 3
3
Step 3
C sits opposite A. In 6-person circle, opposite of position 1 is position 4. So C at position 4
4
Step 4
D sits immediately left of C. Left of position 4 is position 3. But B is already there. This means left of C is position 5. Wait - let me recalculate. If we number 1,2,3,4,5,6 clockwise, then left of 4 is position 3. Since B occupies 3, there's a contradiction. Let me recheck: immediate left of position 4 is position 5 (going anti-clockwise). So D at position 5.
5
Step 5
Remaining positions are 2 and 6. E and F occupy these.
Answer: E sits at either position 2 or 6.
Worked Example 2: Seven people sit in a circle. P sits third to the right of Q. R sits second to the left of P. How many people sit between Q and R when counted clockwise from Q?
Solution Step-by-Step:
1
Step 1
Fix Q at position 1
2
Step 2
P sits third to right of Q, so P at position 4
3
Step 3
R sits second to left of P. Left of position 4 going anti-clockwise: position 3 is first left, position 2 is second left. So R at position 2
4
Step 4
Count from Q(position 1) to R(position 2) clockwise: only position 7 comes between them
Answer: 1 person sits between Q and R.
Shortcut Trick 3 - The Gap Counting Formula: To count people between positions A and B clockwise: if B > A, count = B - A - 1. If B < A, count = n - A + B - 1 (where n is total people).
Most Common Trap: Students often confuse 'left' and 'right' directions. Remember: in clockwise numbering, right means higher numbers, left means lower numbers. Also, 'second to the right' means there's one person in between, not sitting in the second chair. Many students miss this and count wrong positions.
Key Points to Remember
Always fix one person's position first to avoid rotational confusion
In circular arrangement of n people, total arrangements = (n-1)!
Opposite position formula: if person at position x, opposite at x + n/2 (for even n)
Second to the right means one person sits in between, not the second position
Clockwise numbering: right = higher numbers, left = lower numbers
Gap counting formula: between A and B clockwise = B-A-1 (if B>A)
For odd number of people, no one sits exactly opposite to anyone
Adjacent means immediate left or immediate right neighbor only
Use elimination method when multiple conditions are given
Draw the circle and number positions 1,2,3... for visual clarity
Exam-Specific Tips
Circular arrangements of n distinct objects = (n-1)! permutations
In 6-person circle, opposite positions are (1,4), (2,5), (3,6)
In 8-person circle, positions 1 and 5 are diametrically opposite
SSC CGL typically gives 6-8 people in circular seating questions
Maximum people between any two positions in n-person circle = n-3
In odd-numbered circles (5,7,9 people), no exact opposite positions exist
Most SSC circular arrangement sets contain 3-5 questions with 4-6 conditions
Immediate left of position 1 in n-person circle is position n
Practice MCQs
Circular Seating Arrangement — Practice Questions
6graded MCQs · easy to hard · full solution & trap analysis
Five friends – Arun, Bhavna, Chitra, Deepak, and Esha – sit around a circular table. Arun sits immediately to the right of Bhavna. Chitra sits immediately to the right of Arun. Deepak sits immediately to the right of Chitra. Where does Esha sit?
Practice 2easy
Six people sit around a circular table. If we count clockwise from person A, person B is 2 positions away, person C is 4 positions away, and person D is 5 positions away. How many people sit between person D and person B when counting clockwise from D to B?
Practice 3medium
Six friends A, B, C, D, E, and F sit around a circular table. A sits second to the left of B. C sits third to the right of B. D sits between E and F. E sits to the immediate right of A. Who sits to the immediate left of C?
Practice 4medium
Eight people sit around a circular table facing the center. P is fourth to the right of M. Q is third to the left of M. R sits between P and Q (on the side closer to Q). How many people sit between R and Q in the clockwise direction?
Practice 5medium
Five people W, X, Y, Z, and V sit in a circle facing inward. X sits second to the right of W. Y sits immediate left of W. Z sits second to the left of W. Where does V sit relative to W?
Practice 6hard
Eight friends—Arun, Bhavna, Chetan, Deepa, Esha, Faisal, Gaurav, and Hina—sit in a circle facing the center. Arun sits third to the right of Bhavna. Chetan sits second to the left of Deepa. Esha sits immediately to the right of Arun. Faisal sits third to the left of Gaurav. Hina sits immediately to the left of Bhavna. If Gaurav sits second to the right of Chetan, who sits immediately to the right of Deepa?
60-Second Revision — Circular Seating Arrangement
Remember: Fix one person first, then arrange others relative to that position
Formula: Opposite position = current position + n/2 (for even n only)
Trap: 'Second to right' means one person between, not second position
Trick: Number positions 1,2,3... clockwise for systematic solving
Direction: Right = clockwise = higher numbers, Left = anti-clockwise = lower numbers
Gap formula: People between A and B = |B-A|-1 positions
Quick check: Total positioned people should equal given number