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Missing Rank Puzzle

Introduction

Missing Rank puzzles give partial ranking information (some positions or relationships) and ask you to deduce a missing rank - a person's position, who is between two people, or the total number of items.

This pattern is important because it trains you to combine partial orders, reason with constraints, and spot implicit information that completes the ranking.

Pattern: Missing Rank Puzzle

Pattern

Key idea: Turn each clue into an inequality or position constraint, merge them carefully, and use any implicit counts (gaps, ends, opposites) to find the missing rank.

Typical approaches:

  • Translate relative clues to simple comparisons (A > B or A is 3rd from left).
  • Use totals (n) and the formula when positions from both ends are given: Total = Left position + Right position - 1.
  • Place anchor blocks (e.g., A-B-C) and shift them when new clues appear.

Step-by-Step Example

Question

In a row of students, A is 5th from the left and B is 4th from the right. C is just left of B. There are 10 students in the row. What is C's position from the left?

Solution

  1. Step 1: Write the known positions

    A = 5th from left. B = 4th from right (in a row of 10).

  2. Step 2: Convert B's right position to left position

    Left position of B = Total - Right position + 1 = 10 - 4 + 1 = 7th from left.

  3. Step 3: Use the relation between B and C

    C is just left of B → C is one position to the left of B. So C = 7 - 1 = 6th from left.

  4. Final Answer:

    6th from left

  5. Quick Check:

    Positions 1-10: A at 5, C at 6, B at 7 - C is immediately left of B and B is 4th from right (10 - 7 + 1 = 4) ✅

Quick Variations

1. Missing single person's rank when several relative positions are given.

2. Find total number when two positions from opposite ends and an in-between count are given.

3. Two people swap positions - deduce new ranks.

4. Middle position missing (even/odd totals) - identify one or two middle ranks.

Trick to Always Use

  • Step 1 → Convert any "from right" position to "from left" when a total is known: Left = Total - Right + 1.
  • Step 2 → Anchor fixed positions first (ends, opposites, absolute ranks) and place flexible blocks around them.
  • Step 3 → Count gaps explicitly when asked "how many between": Difference - 1.
  • Step 4 → For even totals, remember there are two middle positions: n/2 and (n/2)+1.

Summary

Summary

  • Translate every clue into a concrete position or inequality.
  • Use the formula Total = Left + Right - 1 to switch ends when needed.
  • Anchor fixed positions first and then place relative blocks; count gaps as Difference - 1.
  • Always perform a quick check by reconstructing positions to confirm no clue is violated.

Example to remember:
If B is 4th from right in 10 people, B is 10 - 4 + 1 = 7th from left - use this to place adjacent persons correctly.

Practice

(1/5)
1. In a line of 18 people, Ankit is 6th from the left and Priya is 5th from the right. How many people are between them?
easy
A. 7
B. 8
C. 6
D. 9

Solution

  1. Step 1: Convert Priya’s position from right to left

    Left position of Priya = Total - Right + 1 = 18 - 5 + 1 = 14th from left.

  2. Step 2: Count people between

    People between = 14 - 6 - 1 = 7.

  3. Final Answer:

    7 people → Option A

  4. Quick Check:

    Positions 6th and 14th → persons 7th-13th (7 people) lie between ✅
Hint: Convert right ranks to left (Total - Right + 1), then subtract and minus one.
Common Mistakes: Forgetting to subtract 1 after taking the difference.
2. In a class of 25 students, Rahul is 9th from the top and Meena is 10th from the bottom. Find the total number of students between them.
easy
A. 5
B. 6
C. 7
D. 8

Solution

  1. Step 1: Convert Meena’s bottom rank to top rank

    Meena’s top position = 25 - 10 + 1 = 16th from top.

  2. Step 2: Calculate number between

    People between = 16 - 9 - 1 = 6.

  3. Final Answer:

    6 students → Option B

  4. Quick Check:

    Positions 9th and 16th → 10th-15th inclusive = 6 students ✅
Hint: Convert both ranks to the same direction, then subtract and minus one.
Common Mistakes: Mixing up top and bottom directions when converting positions.
3. A is 8th from the left end and B is 9th from the right end in a row of 20 people. How many people are between A and B?
easy
A. 2
B. 4
C. 3
D. 5

Solution

  1. Step 1: Convert B’s right position to left

    Left position of B = 20 - 9 + 1 = 12th from left.

  2. Step 2: Count people between

    People between = 12 - 8 - 1 = 3.

  3. Final Answer:

    3 people → Option C

  4. Quick Check:

    Positions 9th-11th are between A(8th) and B(12th) → 3 people ✅
Hint: Always convert right-side ranks using Total - Right + 1 before subtracting.
Common Mistakes: Subtracting without converting the right-side rank first.
4. In a class, Riya is 8th from the top and 5th from the bottom. Find the total number of students in the class.
medium
A. 11
B. 12
C. 13
D. 14

Solution

  1. Step 1: Apply the formula

    Total students = Top position + Bottom position - 1 = 8 + 5 - 1 = 12.

  2. Step 2: Verify

    Riya being 8th from top and 5th from bottom fits in a class of 12: top positions 1-12 place Riya at 8 and 5 from bottom = 12 - 8 + 1 = 5.

  3. Final Answer:

    12 students → Option B

  4. Quick Check:

    8 + 5 - 1 = 12 ✅
Hint: Use Total = Top + Bottom - 1 when both directions are given.
Common Mistakes: Forgetting to subtract 1 after adding the two positions.
5. In a queue, A is 6th from the front, and B is 8th from the back. If there are 15 people, find B’s position from the front.
medium
A. 7
B. 10
C. 9
D. 8

Solution

  1. Step 1: Write the given data

    Total people = 15, B is 8th from the back.

  2. Step 2: Convert back position to front position

    B’s front position = Total - Back + 1 = 15 - 8 + 1 = 8th from front.

  3. Step 3: Verify with the total count

    Front 8th means there are 7 people before B and 7 behind (since 15 - 8 = 7).

  4. Final Answer:

    8th from front → Option D

  5. Quick Check:

    If B is 8th from front, then from back = 15 - 8 + 1 = 8 → correct ✅
Hint: Convert back to front using Total - Back + 1.
Common Mistakes: Forgetting to add 1 after subtracting from the total.

Mock Test

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