In this interview, you will be presented with a mathematical challenge that involves exploring a grid-based scenario, which is relevant to understanding patterns and permutations in quantitative finance. You'll need to apply combinatorial thinking and problem-solving skills to identify the number of ways certain conditions can be met on a structured path. This task will test your analytical abilities to reason through constrained movement within defined boundaries. Assistance is available if you require hints to progress. Once you arrive at a solution, you'll have a chance to articulate how you approached and resolved the problem.

Citadel: 2D Paths

Consider all possible paths in a 2D game