Puzzles (Linear and Circular)

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

A puzzle gives a fixed set of people (in most keys 4–7) and a list of positive/negative clues telling you who sits where, next to whom, or at which end. Linear arrangements place entities in a row with definite first/last positions; circular arrangements place them around a closed loop where only left/right neighbours matter.

Anchor the diagram with any exact-position clue (“B is second from the left”) first.
Apply negative clues (“A is not next to D”) to eliminate seating options.
Resolve either-or clues by testing which case contradicts a definite clue.
In circular puzzles, fix an absolute facing direction (e.g., facing the centre) before reading any left/right clue.
For NAT-I (NTS), expect 2–4 MCQs of this type, ~30 seconds each.

Arrangement type	Defining feature	Anchor clue style
Linear	Two definite ends	”X is at the left end”
Circular	No ends; only neighbours	”X is to the immediate left of Y”

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

What makes a puzzle different from other reasoning items

A puzzle supplies a complete set of entities plus a closed list of constraints that together admit one unique arrangement. Every clue must be used at least once; if a clue is redundant, the setter rarely includes it. NAT-I items in standard papers use 5–7 entities to keep the search space manageable inside a 30-second window.

Building the diagram

Start by listing entities down the page. Mark any clue that names a specific seat (“A sits at the right end”, “C is third from the left”) and pencil that entity in. Then walk through the remaining clues in this order:

Exact-position clues — fix the seat.
Neighbour clues (“immediately left/right of”) — fix the adjacent seat.
Negative clues (“is not next to”, “does not sit at”) — cross out impossible cells.
Either-or clues — hold two possibilities; reject the one that breaks a later definite clue.
Conditional clues (“if A is at an end, then B is next to C”) — apply only after the condition is true.

Linear vs circular: the rules that diverge

Feature	Linear row	Circular table
Endpoints	Two (first, last)	None
”Left of” reference	Subject’s left (facing the row)	Subject’s left (facing the centre)
Absolute direction	Fixed	Must be fixed before reading clues
Opposite pairs	Not applicable	n/2 pairs (e.g., 3 pairs in 6 seats)
Equivalent diagrams	Unique reading	Two (rotated 180°) are the same

Quick solving checklist

Write down entities as fixed-position or variable before reading clues.
Count remaining free seats after each anchor to avoid over-constraining.
Re-read the question stem — the answer is in many papers a position, not the full chart.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge cases that break the simple model

Face-in vs face-out circular. If all people face the table centre, their left is your right as you look down. If they face outwards, left and right flip. Mis-reading this is the single most common circular-puzzle error on NAT-I.
Opposite seats for even n greater than 6. In an 8-person table, the person 4th clockwise from A is opposite A, not 3rd. General rule: the k-th person clockwise is opposite A when k = n/2.
Combined sub-loops. A 7-person puzzle can place 3 of them around a small inner circle while the other 4 sit in a row. Solve the inner circle first to free variables, then drop the block into the outer arrangement.
Either-or groups of three. When “A is either at position 1 or at position 5” appears, treat each as a separate branch and discard the branch that later forces a contradiction.

Worked micro-example (5 people, circular, facing centre)

Clues: (i) B is immediately left of A. (ii) D is opposite A. (iii) C is not next to B. (iv) E is to the right of D.

Place A at seat 1, B at seat 5 (immediate left, facing centre). D opposite A → seat 4. E to the right of D → seat 3. C occupies the remaining seat 2. Check (iii): C (seat 2) is not adjacent to B (seat 5) — true. Unique arrangement confirmed.

Common mistake audit

Mistake	Why it fails	Fix
Treating viewer’s left as subject’s left	Breaks every neighbour clue	Always declare facing direction first
Forgetting circular has no ends	Forces an impossible “first”	Use only neighbour relations
Locking either-or without re-checking	Misses a later contradiction	Hold both branches, discard after all clues
Miscounting opposite seat	Wrong n/2 calculation	n/2 rule, then verify

Exam strategy for NAT-I

Puzzle items account for roughly 4% of the Analytical Reasoning MCQ block. Allocate no more than 45 seconds per item: draw a tiny circle, anchor one clue, and scan the options — most wrong answers fail the first negative clue you apply. If two options both survive, apply the either-or or conditional clue that the setter placed last in the list.

Practice prompts

Seven friends A–G sit around a circular table facing the centre. A is 2nd to the left of B; C is opposite G; D is immediately right of A. Who is opposite F?
Five people stand in a row. P is not at either end. Q is immediately to the left of R. S is at the right end. T is between P and Q. Find the person at the left end.

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Puzzles (Linear and Circular)