In the square grid shown on the left, a person standing at P2 position is required
to move to P5 position.
The only movement allowed for a step involves, “two moves along one
direction followed by one move in a perpendicular direction”. The permissible
directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions
marked X on the right.
Without occupying any of the shaded squares at the end of each step, the
minimum number of steps required to go from P2 to P5 is
1
2
3
4
5
P
Q
R
S
T
Example: Allowed steps for a person at Y
Options:
(A) 4
(B) 5
(C) 6
(D) 7
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2022 Q.9)**
**1. Governing Concept**:
- **Topic**: Spatial Aptitude & Grid Pathfinding (Knight's Move)
- The move described ("two steps along one direction followed by one perpendicular step") is the standard chess Knight (L-shape) move $( \pm 2, \pm 1 )$ or $( \pm 1, \pm 2 )$.
- Navigating from $P2$ to $P5$ on the grid without traversing any shaded obstacle squares requires evaluating minimum valid knight-moves, yielding minimum steps $= 5$ (Option B).
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Path blocked by shaded obstacle squares.
- **Option (B) is CORRECT**: Shortest unblocked valid Knight-move path on the grid.
- **Option (C) is INCORRECT**: Suboptimal path.
- **Option (D) is INCORRECT**: Redundant moves.
**3. Final Answer**:
- **Correct Choice**: **B**
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