Checker Ends in Top Corner on 5x5

This interview question is about a random walk on a discrete grid with strict movement rules and a constrained starting region. It mixes geometric structure with probability, requiring you to think about how paths evolve on a checkerboard when only certain diagonals are allowed. Within quant prep, it sits at the intersection of combinatorics, probability, and symmetry arguments, framed in a clean, puzzle-style setting.

It trains your ability to model constrained stochastic processes, translate a word problem into a state-space representation, and keep track of reachable states over time. You practice counting structured paths, reasoning about absorbing endpoints, and aggregating path probabilities. It also sharpens your skill at spotting invariants and symmetries that simplify otherwise messy enumerations in quant interviews.

This matters in quant interviews because many trading and risk problems reduce to constrained Markovian dynamics on a lattice-like state space. Interviewers use this kind of random-walk question to see if you can do rigorous quant prep: build a clean mathematical model, manage combinatorial explosion, and compute a nontrivial probability quickly and accurately under pressure.

What it tests

This class of problems is governed by the principle of constrained random walks on a lattice, where the set of allowed moves and the geometry of the board determine which endpoints are reachable from a given starting position. The key insight is that, although each move is random, the structure of the grid and the movement rules restrict the set of possible paths, often reducing the problem to counting the number of valid paths that reach a target under these constraints. The probability of reaching a specific endpoint is then the sum over all valid paths, weighted by the probability of each path (typically $1/2^n$ for $n$ moves with two choices per move), normalized by the number of starting positions. This approach generalizes to any grid or movement rule: enumerate the ways to reach the target, account for the constraints, and sum the probabilities accordingly. The symmetry or lack thereof in the board or movement rules can often be exploited to reduce computation or to spot unreachable cases quickly.