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Order and Ranking Puzzle

Introduction

Order and Ranking Puzzles involve arranging people or objects according to their positions, scores, heights, or other measurable attributes. These questions are extremely common in competitive exams to test your logical ordering and positional reasoning skills.

You may be asked to find rank from top or bottom, total number of persons, or the position between two ranks - all of which require a consistent logic approach.

Pattern: Order and Ranking Puzzle

Pattern

The key idea is to convert given positional data into a visual sequence and apply formulas for missing rank, total count, or position between two ends.

Typical clue types include: 1️⃣ “A is 6th from the top, B is 10th from the bottom in a class of 20.” 2️⃣ “Find how many students are between A and B.” 3️⃣ “Find total number of students in the group.”

Step-by-Step Example

Question

In a row of students, A is ranked 8th from the top and 13th from the bottom. How many students are there in the row?

Options:

  • A) 19
  • B) 20
  • C) 21
  • D) 22

Solution

  1. Step 1: Use the rank-sum relation

    The total number of students = (Rank from top + Rank from bottom - 1).

  2. Step 2: Substitute values

    Total = 8 + 13 - 1 = 20.

  3. Final Answer:

    20 → Option B

  4. Quick Check:

    If A is 8th from top and 13th from bottom, 7 above and 12 below → total = 20 ✅

Quick Variations

1️⃣ Finding total number of persons using both top and bottom ranks.

2️⃣ Finding rank from one side given total and other-side rank.

3️⃣ Finding number of persons between two ranks.

4️⃣ Comparison-type (e.g., A is 3rd taller than B).

Trick to Always Use

  • Step 1: Draw a visual number line (Top → Bottom) to avoid confusion.
  • Step 2: Use the universal formula: Total = (Rank from Top + Rank from Bottom - 1).
  • Step 3: For “between two persons”, use Difference - 1.
  • Step 4: Re-check that rank directions (top/bottom or left/right) are consistent.

Summary

Summary

  • Translate rank clues into numeric equations or sequences.
  • Use the core rank-sum formula to find total count.
  • To find ranks from the opposite end, use: Rank from bottom = Total - Rank from top + 1.
  • Always visualize the sequence with small examples to avoid reversal errors.

Example to remember:
If a student is 7th from the top and 14th from the bottom, total = 7 + 14 - 1 = 20 students.

Practice

(1/5)
1. In a row of students, X is 5th from the top and 12th from the bottom. How many students are there in the row?
easy
A. 16
B. 17
C. 18
D. 19

Solution

  1. Step 1: Use the rank-sum formula

    Total = (Rank from top + Rank from bottom - 1).

  2. Step 2: Substitute values

    Total = 5 + 12 - 1 = 16.

  3. Final Answer:

    16 → Option A

  4. Quick Check:

    If there are 16 students, X is 5th from top → 4 above and 11 below → 12th from bottom ✅
Hint: Always apply Total = (top rank + bottom rank - 1) for direct rank pairs.
Common Mistakes: Forgetting to subtract 1 when adding ranks from both ends.
2. In a line of 30 students, A is 7th from the top and B is 3rd from the top. How many students sit between A and B?
easy
A. 3
B. 4
C. 5
D. 6

Solution

  1. Step 1: Identify positions from the same end

    A is 7th from top, B is 3rd from top (B is above A).

  2. Step 2: Calculate students between

    Positions: B at 3, then 4, 5, 6, A at 7 → students at positions 4, 5, 6 → 3 students.

  3. Step 3: Use the formula

    Number between = |7 - 3| - 1 = 4 - 1 = 3.

  4. Final Answer:

    3 → Option A
Hint: When both ranks are from the same end, use |rank1 - rank2| - 1.
Common Mistakes: Forgetting to subtract 1, which counts the endpoints themselves.
3. There are 25 candidates. C is 9th from the top. What is C’s rank from the bottom?
easy
A. 15th
B. 16th
C. 17th
D. 18th

Solution

  1. Step 1: Use conversion formula

    Rank from bottom = Total - Rank from top + 1.

  2. Step 2: Substitute values

    Rank from bottom = 25 - 9 + 1 = 17 → 17th.

  3. Final Answer:

    17th → Option C

  4. Quick Check:

    If C is 9th from top, there are 8 above and 25 - 9 = 16 below → rank from bottom = 16 + 1 = 17 ✅
Hint: Always use Total - topRank + 1 to convert ranks between ends.
Common Mistakes: Forgetting the +1 when converting ranks.
4. In a row, A is 11th from the top and B is 17th from the bottom. If A is above B and there are 4 students between them, how many students are in the row?
medium
A. 28
B. 29
C. 30
D. 32

Solution

  1. Step 1: Let total = T and convert B’s top rank

    B from top = T - 17 + 1 = T - 16.

  2. Step 2: Use the gap relation (A above B)

    Number between = (top rank of lower person) - (top rank of higher person) - 1. So (T - 16) - 11 - 1 = 4 ⇒ T - 28 = 4.

  3. Step 3: Solve for T

    T = 32.

  4. Step 4: Verify the original clues

    If T = 32, B from top = 32 - 16 = 16, so positions are A = 11 and B = 16 → people between = 12,13,14,15 = 4. Also B from bottom = 32 - 16 + 1 = 17 → matches given '17th from the bottom'.

  5. Final Answer:

    32 → Option D

  6. Quick Check:

    T = 32 ✅ A at 11th from top ✅ B at 16th from top which is 17th from bottom ✅ exactly 4 between (12-15) ✅
Hint: Convert the bottom-given rank to its top-rank expression (T - bottom + 1), then use (difference - 1) = number between to solve for T.
Common Mistakes: Forgetting the -1 in the 'between' formula or failing to explicitly re-check the bottom-given rank after solving for T.
5. In a row, X is 14th from the left and Y is 20th from the left. There are 5 people between X and Y. If X is to the left of Y, how many people are there in the row (minimum consistent total)?
medium
A. 20
B. 21
C. 22
D. 23

Solution

  1. Step 1: Both ranks given from left

    X = 14th, Y = 20th.

  2. Step 2: Verify the number between

    Number between = |20 - 14| - 1 = 6 - 1 = 5 → matches given data.

  3. Step 3: Determine minimal total

    The highest given position is 20 (Y). If no person is specified after Y, the minimal consistent total = 20.

  4. Final Answer:

    20 → Option A
Hint: When both ranks are from same side, the maximum rank given is a lower bound for total; verify gaps first, then decide if additional people after the higher rank are required.
Common Mistakes: Adding the 'between' people again to the higher rank (double-counting).

Mock Test

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