Ranking and Arrangement
About 7 min · Logical Reasoning · English
Time worked out from the lesson's 473 words at 150 words a minute, plus a minute for each question.
Ranking and Arrangement is a Logical Reasoning topic in SOF IMO that tests your ability to organize information logically. These problems appear in two main flavors: ranking problems (determining positions in a queue, class or competition from clues like "5th from top" or "12th from bottom") and arrangement problems (seating people in a row or around a table based on conditions like "A sits two places left of B").
Key ideas
- Ranking from top and bottom: If someone is nth from top and mth from bottom in a queue, total people = n + m − 1 (subtract 1 to avoid counting that person twice).
- Linear arrangement: People or objects seated in a straight row, facing a direction (usually north). "Left" and "right" are relative to the person's viewpoint when facing that direction.
- Circular arrangement: Seating around a table—clockwise/anticlockwise matters, and there's no absolute "first" position. If all face center, "left" means clockwise neighbor; if facing outward, "left" means anticlockwise neighbor.
- Fixed reference point: Always anchor your diagram to a fixed person or position mentioned in the problem. Place them first, then position others relative to them.
- Immediate vs. positional neighbors: "Next to" means immediately adjacent (one seat away). "Two places to the left" means one person in between.
Watch out for
- Counting the person twice: Forgetting to subtract 1 in rank-from-top plus rank-from-bottom. The person himself is counted in both, so total ≠ n + m but n + m − 1. Fix: Always subtract 1 in overlap formulas.
- Left-Right confusion: Mixing up left/right when people face north vs. south, or in circular arrangements. Fix: Draw a small compass rose or label "Facing North" clearly. Remember facing north means left = west = your diagram left.
- Off-by-one in "between" counting: If A is at position 3 and B at position 6, students between = 6 − 3 − 1 = 2 (positions 4 and 5 only). Students often forget the −1. Fix: Positions between p and q (q > p) is q − p − 1.
Quick reference
- Total in queue = (rank from top) + (rank from bottom) − 1.
- People between positions a and b = |b − a| − 1.
- Linear row facing north: left = west, right = east.
- Circular facing center: right neighbor = anticlockwise, left = clockwise.
- Always draw a diagram—never solve ranking/arrangement purely in your head.
Check yourself: 3 questions
1. In a class of 45 students, Rahul's rank from the top is 18th. What is his rank from the bottom?
2. In a row of 60 students, Mohan is 23rd from the left end and Sohan is 34th from the right end. How many students are there between Mohan and Sohan if they interchange their positions?
3. In a class of 40 students, Amit ranks 7th from the top. What is his rank from the bottom?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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