Height
Taller/shorter clues; tallest, shortest, middle.
Height
Height Ranking Problems
What you'll learn
- Order people by taller/shorter clues.
- Find tallest, shortest, and middle from partial clues.
- Draw a height line or table to organise clues.
- Handle ties when two people are equal height.
Key concepts
Level 1 — Transitive clues
If A > B and B > C, then A > C (A tallest of the three).
Level 2 — Partial order
Clues may not give full order — use elimination.
Level 3 — Tallest / shortest
Collect all "X is taller than Y" clues; person never on the shorter side → likely tallest.
Level 4 — Indian context
In a school assembly line in Pune, four students compare heights after PT class — arrange from clues.
NCERT anchor: CBSE Class 4 logical reasoning; Math-Magic 4 Ch 12 — comparing measurements
Worked example
A is taller than B. B is taller than C. Who is shortest?
Step 1 — Order: A > B > C.
Step 2 — Lowest on list = shortest.
Answer: **C**
Ram is taller than Shyam. Anil is shorter than Shyam. Order from tallest.
Step 1 — Ram > Shyam > Anil.
Answer: **Ram, Shyam, Anil**
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Assuming tallest is first mentioned | First name not always tallest | Build full order from all clues |
| Ignoring 'shorter than' direction | Reversing inequality | A shorter than B → B is taller |
| Forgetting ties | Two same height | If A = B in height, they share a rank |
| Using age instead of height | Mixed attribute | Use only height clues for height ranking |
Quick check
- A > B, B > C — tallest?
- Ram > Shyam, Anil < Shyam — order?
- Draw height line for 3 people.
- Stretch: Five students — you know four pairwise comparisons. Can you always find the tallest? Try a case where you cannot.
Revision tip: Draw a vertical line — higher = taller; place names as you read each clue.
Open the Practice tab for graded questions on Height Ranking Problems.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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