Frog and Pond

What this combinatorial path-counting question tests

This is a medium-difficulty combinatorics problem that appears in probability and quantitative reasoning interviews. It tests your ability to set up and solve a constrained counting problem—specifically, how to enumerate all valid paths subject to multiple rules without double-counting or missing cases.

The core skill is translating word constraints into a mathematical model. Here, you must decide whether to use direct enumeration, recursion with memoization, or a generating-function approach. The problem rewards clarity in defining what constitutes a "unique way" and careful bookkeeping of the constraints (jump size bounds, mandatory intermediate steps, starting and ending positions).

• Recursion and dynamic programming for path counting
• Constraint satisfaction and state representation
• Combinatorial enumeration without overcounting