Shortest Path
Count minimum blocks on a grid — no unnecessary detours.
Shortest Path
Shortest Path
What you'll learn
- On a grid, move along lines — no diagonal shortcuts unless allowed.
- Shortest path = fewest steps/blocks.
- Count Manhattan distance: right + up blocks only.
- Avoid unnecessary detours in puzzles.
Key concepts
Level 1 — Core idea
Verbal: From home to shop 3 blocks east and 2 north — one shortest route is 5 moves.
Symbolic: Shortest steps = |Δeast| + |Δnorth| on grid.
Visual: City block grid — trace L-shaped path.
Level 2 — Going deeper
Many shortest paths exist (zigzag same length). Do not go past target and back — wastes steps.
NCERT anchor
NCERT Math Mela, Chapter 4 grid patterns support path counting. Use squared notebook.
Worked example
Start (0,0), end (3,2) — minimum blocks?
Step 1 — Move 3 east + 2 north (or interleave)
Step 2 — Total = 3 + 2 = **5 blocks**
Answer: **5** minimum ✓
Go 2 east, 1 north, then 1 west — at end, how far from start?
Step 1 — Net east: 2−1 = **1**
Step 2 — Net north: **1**
Step 3 — Shortest back = 1+1 = **2** blocks (not path taken length)
Common mistakes
| Mistake | Why | Fix |
|---|---|---|
| Diagonal one step | Grid rule ignored | Unless stated, along grid lines |
| Count turns not blocks | Wrong unit | Count each edge step |
| Longer scenic route | Detour accepted | Minimum = no extra loops |
| Add all moves including backtrack | Gross vs net | For distance, use net displacement |
Quick check
- 2 east + 2 north — min steps?
- Why avoid detours?
- Draw 3×3 grid shortest corner to corner.
- Stretch: How many different shortest paths 2 east + 2 north? (6 — intro)
Revision tip: Mark start and end dots; only move toward target each step for shortest path.
Open the Practice tab for graded questions on Shortest Path.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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