Circular and Polygonal Arrangements

Around a circle, when a person faces the CENTRE (inward), their LEFT is clockwise and right is anticlockwise. When facing OUTWARD, it flips: left is anticlockwise, right is clockwise. In mixed-facing circles, this is the #1 trap. Speed method: draw the circle, mark each person's facing with an arrow, then for every 'left/right' clue, decide direction PER PERSON using their own arrow. Memory aid: 'IN-Left-Clock' (Inward → Left = Clockwise). For all-inward problems (most common), just remember left = clockwise throughout. Always count gaps, not people, when a clue says 'third to the left'.

Square/rectangular tables seat people at CORNERS (facing centre) and MIDDLE-of-SIDES (facing outward) in SBI PO 'mixed direction' puzzles. A common 8-person square: 4 at corners face centre, 4 at side-middles face outward. Corner people and side people have DIFFERENT left/right orientation — handle separately. For 'between' clues across a corner, count along the perimeter. Speed aid: number positions 1-8 going clockwise; convert all 'left/right' to clockwise/anticlockwise steps using each seat's facing. Memory hook: corners 'look in', edges 'look out'. Diagonally opposite corners are 4 perimeter-steps apart on an 8-seat square.

Circular seating puzzles waste more time in SBI PO than they should, mostly because aspirants count seats one by one in two different ways. A small dual-direction shortcut clears half of that confusion in seconds.

This lesson teaches you the gap-counting shortcut for circular arrangements — a way to convert any "Kth to the right" clue into the equivalent "Kth to the left" clue, and use that to cross-check clues, spot contradictions early and lock seats faster.

Definition: A circular arrangement is a seating where n people sit around a round table or circle, so that the "first" and "last" seats are next to each other.

Definition: "A is Kth to the right of B" means: start at B, move K seats in the clockwise direction (when people face the centre) and you land at A. "Kth to the left" is the same idea, but anticlockwise.

The key idea: same seat, two names

In a straight row of n chairs, "3rd to the right of B" and "3rd to the left of B" point to two different seats. In a circle of n people, the two directions wrap around and eventually meet. That means each seat has two valid descriptions from any reference person — one clockwise, one anticlockwise — and the two numbers always add up to n.

Formally: in a circle of n people, "Kth to the right of B" and "(n - K)th to the left of B" describe the same seat.

A small numerical check makes this stick. Imagine 8 friends sitting around a round table for a chai meet. Number the seats 1 to 8 going clockwise, with B at seat 1. The 3rd seat clockwise from B is seat 4. Now count anticlockwise from B: seat 8, seat 7, seat 6, seat 5, seat 4. That is 5 steps anticlockwise to reach the same seat. And indeed 3 + 5 = 8 = n. Once you see this once, you can rewrite any awkward clue into the direction your diagram already shows.

Why it matters in SBI PO

Banking aspirants will see four to five linked puzzles in the reasoning section, and at least one is almost guaranteed to be a circular arrangement of 8 or 10 people, often with mixed-direction facing (some inward, some outward). Examiners love giving clues from inconvenient directions on purpose. The shortcut does two things:

First, it standardises the puzzle. Pick one direction — say "to the right" — and rewrite every clue in that direction using the n - K trick. Now every clue is in the same language, and you can match them quickly.

Second, it gives you a free contradiction check. If two independent clues tell you "A is 3rd to the right of B" and "A is 4th to the left of B" in a circle of 8, you instantly see that 3 + 4 = 7 ≠ 8, so the puzzle is inconsistent — unless a third clue (like extra people or empty seats) changes n. Spotting this in 10 seconds saves you from drawing three wrong diagrams.

Real-world example

In a circle of 10 SBI PO interview candidates seated around a round table for a group discussion, the moderator notes: "Rohan is 4th to the right of Priya." A second observer notes: "Rohan is 6th to the left of Priya." Are these consistent?

Check: 4 + 6 = 10 = n. Yes, perfectly consistent — both observers are describing the same seat, just from opposite directions. If the second observer had said "5th to the left", the sum would be 9, not 10, and one of the two facts would have to be wrong.

Worked example

Question: In a circle of 8 people facing the centre, B is sitting at a fixed seat. Where does "5th to the left of B" sit, and what is the equivalent "Kth to the right" description?

Solution:
Step 1: n = 8. The shortcut says "Kth to the left of B" = "(n - K)th to the right of B".
Step 2: With K = 5 and n = 8: (n - K) = 8 - 5 = 3.
Step 3: So "5th to the left of B" = "3rd to the right of B".
Conclusion: Both phrases lock on to the same seat. While drawing the diagram you can mark it from whichever side is closer to B in your existing setup.

A small but powerful sanity check

Once you have a partial diagram, every fresh clue is either compatible or it is not. The gap-counting shortcut gives you a one-line test:

"Two clues about A relative to B from both sides are consistent only if their numbers sum to n."

Use this before you redraw. If a clue says "A is 4th to the left of B" and another says "A is 5th to the right of B" in a circle of 8, the sum is 9, not 8 — something is off. Either you misread one clue, or the puzzle uses a different n (perhaps two empty seats hidden in the wording), or the puzzle is internally inconsistent (rare in SBI PO but possible in mocks).

Common misconception: Students often assume that "left" and "right" in a circle behave like they do in a straight row, where they are mirror opposites. They are not. In a circle, "left" and "right" are just the two ways of walking around the same loop, and they always add up to n for any pair of seats. Carrying row intuition into a circle is the single biggest source of silly errors here.

Another common confusion is forgetting whether people face the centre or outward. When everyone faces the centre, your "right" matches the natural clockwise direction in your diagram. When someone faces outward, that person's right is the anticlockwise direction in the same diagram. Always check this once before applying the shortcut; the sum-to-n rule itself does not change, but the direction of counting does.

Circular and polygonal (square/rectangle/triangle/hexagon) arrangements are the highest-frequency puzzle type in SBI PO — at least one 5-mark set in Prelims, often two in Mains. The examiner's whole game is facing direction (centre vs outside), because it silently reverses clockwise/anticlockwise for individual people. SBI raises the bar with mixed in/out facing and a second variable (profession, floor, number).

Core rule

Facing	Person's "left" goes	"right" goes
Facing CENTRE (inward)	clockwise	anticlockwise
Facing OUTSIDE	anticlockwise	clockwise

For polygons, people sit at corners AND mid-sides; read the exact facing rule (e.g. "corner persons face centre, middle persons face outside"). In even circles, "faces/sits opposite" means the diametrically opposite seat (n/2 apart).

Method

Draw the shape, mark facing arrows, anchor the person with the most fixed relation, and count seats in the stated direction for that person's facing. Run Case 1/Case 2 when a gap can be either way.

Exam Tricks & Tips

• 🎯 In an all-inward circle everyone's left = clockwise; the moment one person faces outward, flip only that person's left/right.
• 🎯 "3rd to the left" in a circle of 8 = "5th to the right" (8 − 3); always take the shorter count.
• 🎯 For "faces X" in even circles, jump straight to the opposite seat (n/2 apart) instead of counting one by one.
• 🎯 In polygon sets, first classify each seat as corner or mid-side, then apply the two facing rules — mixing them up is the top error.
• 🎯 If two people face each other across the centre, fixing one instantly fixes the other.
• 🎯 For hexagon/triangle sets, note corner-count vs side-count before placing anyone.
• ❌ Common mistake: calling anticlockwise "left" for an outward-facing person — it is that person's right.

Expected exam pattern

Circle of 8 (all-inward or mixed), or a square with 8 (4 corners + 4 middles), or a hexagon/rectangle with a second attribute. 5 questions: neighbours, "who faces whom", position-count, odd-one-out.

Quick recap

Arrows first, classify seats (corner/mid-side), remember inward-left = clockwise and outward-left = anticlockwise, and use "n minus count" for opposite-direction counting.

Cover the answer, recall, then check. 12 cards on circular & polygonal seating for SBI PO.

Q1. For a person facing the CENTRE, which direction is their left?
A1. Clockwise. Inward-facers: left = clockwise, right = anticlockwise.

Q2. For a person facing OUTSIDE, which direction is their right?
A2. Clockwise. Outward-facers: right = clockwise, left = anticlockwise.

Q3. In a circle of 8, "3rd to the left" equals what count to the right?
A3. 5th to the right (8 − 3 = 5).

Q4. In an even circle, what does "A sits opposite B" mean positionally?
A4. B is diametrically opposite — n/2 = 4 seats away in a circle of 8.

Q5. In a square arrangement, how many seats are corners and how many mid-sides?
A5. 4 corners and 4 mid-side seats (for 8 persons).

Q6. Why fix facing arrows before placing anyone?
A6. Left/right (clockwise/anticlockwise) reverses with facing; a misread arrow corrupts the whole grid.

Q7. All-inward circle of 6: if C is 2nd to the right of A, where is C?
A7. Two seats anticlockwise from A (right = anticlockwise when facing centre).

Q8. How do you handle a set where some face in and some face out?
A8. Apply the standard rule per person, flipping only the outward-facers' left/right individually.

Q9. "A and B face each other across the centre" — what does placing A do?
A9. It instantly fixes B at the diametrically opposite seat.

Q10. Quickest anchor to start a circular set?
A10. The person tied to a fixed relation — "sits opposite X" or a named immediate-neighbour pair.

Q11. In a polygon, what must you decide before applying left/right?
A11. Whether each seat is a corner or a mid-side, since the two groups may face opposite ways.

Q12. Most common circular/polygon error?
A12. Treating anticlockwise as "left" for an outward-facing person — it is that person's right.

Worked Example

Problem: Six friends P, Q, R, S, T, U sit around a circular table facing the centre. P is second to the right of Q. R sits between P and S. T is opposite Q. Who sits immediately to the left of Q?

Solution:
Fix Q's position and place others. Going clockwise (to the right when facing centre):
"P is second to the right of Q" → from Q, skip one seat clockwise; P is two seats clockwise from Q.
"T is opposite Q" → three seats from Q, i.e. directly across.
Place seats 1–6 clockwise from Q: Q(1), seat2, P(3), T(4, opposite Q), seat5, seat6.
"R sits between P and S" → R is adjacent to P; the open seat next to P (seat 2 or seat... ) at seat 2 gives R, and S next to R at seat... but seat before P is seat 2. Put R at seat 2 (between Q and P) — but R must be between P and S, so S at seat... Take R at seat 4? T is there. So R at seat 2 with S needing to be on P's other side (seat 4 = T, taken). Re-place: seats clockwise Q(1), U(2), P(3), R(4)?? T must be opposite Q at seat 4. Resolve: R between P and S with T opposite Q means R and S occupy seats 5 and 6; then U takes seat 2. Immediately left of Q (counter-clockwise, seat 6) is S.

Answer: S sits immediately to the left of Q.