Direction Change

What this direction-change probability question tests

This is a medium-difficulty probability question that combines lattice-path counting with parity reasoning. It appears frequently in quant interviews because it rewards candidates who can think clearly about symmetry and constraint propagation rather than brute-force enumeration.

The core challenge is to count paths with a specific property—an odd number of direction reversals—without listing every path explicitly. Successful approaches typically exploit symmetry or recurrence relations to avoid combinatorial explosion. The question probes whether you can translate a path property into a counting argument, and whether you can reason about parity constraints systematically.

• Lattice paths and their combinatorial structure
• Parity and modular reasoning
• Symmetry arguments to reduce casework
• Recursive or dynamic-programming framing of path problems