6x6 Grid Paths Count

This classic quant prep question is about counting how many ways a constrained process can unfold when each outcome is a sequence of simple steps. The setup uses a grid game to encode a structured combinatorics problem, which is exactly the kind of abstraction that appears in many quant interviews. Top trading firms like this style because it looks simple but reveals how candidates reason about discrete structures.

It trains core combinatorics intuition: recognizing when different paths correspond to arrangements of indistinguishable actions, understanding symmetry, and mapping a story problem into a clean counting framework. It also builds comfort with translating between a geometric picture and a purely algebraic combinatorial object, a recurring theme in quant prep.

This matters in quant interviews because path counting under constraints is a proxy for state-space thinking in stochastic processes, dynamic programming, and lattice models. Interviewers use it to see whether you can quickly identify hidden structure, generalize patterns, and give precise, scalable answers under time pressure-skills that carry over directly to modeling, derivatives pricing, and algorithm design in quantitative finance.

What it tests

This class of problems is governed by the principle of counting permutations of indistinguishable objects: when a process consists of a fixed number of two (or more) types of moves, the total number of unique sequences is given by multinomial coefficients. The key is that each path is uniquely determined by the order in which you interleave the required number of each move type. This arises because the constraints force every solution to use the same multiset of moves, so the only freedom is in their arrangement. The reason this works is that, for each arrangement, the moves themselves are indistinguishable except for their type (up or right), so the count is the number of ways to choose which steps are of each type. This structure appears in grid-walking, word arrangements with repeated letters, and similar combinatorial settings.