Order, Ranking & Seating

Snapshot

• Order, Ranking & Seating covers three close cousins: linear ranking ("how many between…", "rank from both ends"), linear seating (a row, all facing one way), and circular seating (a table, facing the centre or outward).
• Almost every question is solved by drawing the row or circle and filling in fixed positions first, then placing the rest by the clues. The trap is left/right, which flips depending on which way people face.
• This guide gives you the ranking formula, the row and circle methods, the facing rule, and the blood-relation-in-seating twist — with worked examples.
• Exam reality: +5 / −1. Draw the arrangement; never hold it in your head.

Part 1 — Linear ranking

The one formula: in a row of n people, a person who is ath from the left and bth from the right satisfies a + b = n + 1. So "20th from left and 26th from right" means n = 20 + 26 − 1 = 45. For "how many between two ranks", subtract and remove the endpoints.

Part 2 — Seating: rows and circles

Linear (a row). If everyone faces North, then their left is West and their right is East — the opposite of how it looks to you on the page. Draw the row, place the fixed people, then fill by the clues.

Circular (a table). If all face the centre, a person's left is clockwise and right is anticlockwise (mirror of facing-out). Always note the facing direction first. With 6 around a table, "opposite" means 3 seats away.

Part 3 — The facing rule (where marks are lost)

• Facing the same way (a row): left and right are consistent for everyone.
• Facing the centre: left/right are reversed compared with facing out.
• Mixed facing (some in, some out) is the hardest variant — mark each person's facing with a small arrow.

Part 4 — Speed techniques

1. Draw first, always — a circle or a row of dashes.
2. Place the fixed/most-constrained person first, then build outward.
3. Convert "left/right" using the facing rule before placing anyone.
4. For ranking, use a + b = n + 1 — it answers most "total people" questions instantly.
5. "Between" excludes the endpoints; "from a point" includes the start.

Part 5 — Worked examples

1. In a row, Ravi is 7th from left and 9th from right. Total? 7 + 9 − 1 = 15.

2. In a class of 40, a boy is 12th from the top. His rank from the bottom? 40 − 12 + 1 = 29.

3. Six people A–F sit around a table facing centre, A between B and C. To A's immediate left (clockwise) is whichever of B/C the clues fix — draw and place.

4. Five sit in a row facing North. If P is to the immediate left of Q, then on the page P is to the West (left as we look) of Q — consistent because all face us-away.

5. Eight around a circle facing centre; the person 3rd to the right of X sits opposite Y. Draw 8 seats, fix X, count 3 anticlockwise (right when facing centre), mark opposite.

6. A is 15th from left, B is 20th from left in a row of 40. People between them = 20 − 15 − 1 = 4.

7. In a circle of 6 facing the centre, who is opposite the person 2nd to the left of M? 2nd left (clockwise) of M, then +3 seats for "opposite".

8. Row of 7 facing South: now their left is East, right is West — the reverse of the North case; re-map before placing.

Part 6 — Common traps

• Left/right with facing — the single biggest error; fix the facing first.
• Counting "between" with endpoints — exclude them.
• a + b = n + 1, not a + b = n.
• Clockwise vs anticlockwise flips when people face outward.
• Opposite in a circle of n is n/2 seats away (only defined for even n).

Part 7 — How to use this page

Memorise a + b = n + 1 and the facing rule, re-draw the eight examples as rows/circles, then attempt the practice set and the timed test.

One-line revision: draw the row or circle, place the most-constrained person first, map left/right using the facing direction (centre-facing reverses it), and use a + b = n + 1 for totals.