Rabbit's 10-Step Jump Sequences

This combinatorics question is about counting structured paths under restricted moves, a core theme in quant interview prep. You study how many distinct sequences obey a rule about allowable jumps, which forces you to think in terms of compositions of an integer with forbidden parts. It's a classic example of encoding a discrete process as an ordered sequence subject to constraints, which appears often in quant interviews.

It trains your ability to recognize and build recurrences, understand constrained counting, and translate a verbal process into a precise combinatorial model. You practice seeing how a simple-sounding rule on moves reshapes the space of valid sequences and changes familiar integer-sequence behavior.

This matters for quant interviews because many real quant problems become "count the valid configurations under these rules." Success in quant prep requires turning such narratives into clean state definitions and recursive structures, a key skill for trading, risk, and research roles.

What it tests

When a process is constrained by allowed move sizes (such as step sizes in a staircase), the total number of ways to reach a target can be constructed recursively by considering all valid first moves and then counting the ways to complete the remainder. This leads to a recurrence relation where each term represents the sum of the counts for all possible subproblems created by taking each allowed first move. The structure of the allowed moves determines the recurrence: forbidding certain moves (like single steps) shifts or alters the classic recurrence (such as the Fibonacci sequence). The reason this works is that each path to the goal can be uniquely decomposed into its first move and a valid path from the new position, ensuring all possibilities are counted exactly once. This principle applies broadly to problems involving sequences of actions with restricted increments or decrements.