## Problem Two players alternate turns. There is a token on integer position `pos` on a number line. Each turn the current player moves the token left or right by any value in a given set `moves` (e.g., `{1, 3}`). A player who moves the token to position 0 wins. A player who cannot move (or is forced to move off the line) loses. Given `pos` and `moves`, determine if the first player wins with optimal play. ```python def first_player_wins(pos: int, moves: set[int]) -> bool: ... ``` ``` moves = {1, 3}, pos = 4 Winning positions (W) vs losing positions (L): pos=0: W (you just won) pos=1: W (move 1 -> 0) pos=2: L (can go to 1 or ... 1 is W for opponent; -1 invalid) pos=3: W (move 3 -> 0) pos=4: L (move 1->3 W for opp, move 3->1 W for opp) Output: False (first player loses) ``` ## Follow-ups 1. This is a combinatorial game theory problem. Describe the DP recurrence for `is_winning(pos)`. 2. What is the time complexity of your DP solution, and what is the memoization base case? 3. How does the problem change if moves can also increase `pos` (bidirectional movement)? 4. Extend to a 2D grid: the token is at `(r,c)`, allowed moves are `{up, down, left, right}`. The player who reaches `(0,0)` wins. How do you adapt your solution?

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Line Game: Optimal Strategy for a Positional Token-Moving Game on a Number Line

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Problem Two players alternate turns. There is a token on integer position pos on a number line. Each turn the current player moves the token left or right by any value in a given set moves (e.g., {1, 3}). A player who moves the token to position 0 wins. A player who cannot move (or is forced to move off the line) loses. Given pos and moves, determine if the first player wins with optimal play. Follow-ups This is a combinatorial game theory problem. Describe the DP recurrence for is_winning(pos).…

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About Hudson River Trading Interview Reports

This question was reported by a candidate who interviewed at Hudson River Trading. LeakCode aggregates interview reports from 10+ sources, including 1Point3Acres, Glassdoor, LeetCode Discuss, Blind, Reddit, Indeed, and Nowcoder. Each report is translated where necessary, deduplicated against existing entries, and tagged by company, role, round type, and reporting date.

Use this question as one calibration data point, not a memorization target. Companies typically rotate their question pools every 2-4 months; the exact wording of a 2024 question may differ from what you encounter today. The underlying pattern, difficulty level, and follow-up depth at Hudson River Trading are the higher-signal extractions to take from this report.

For broader preparation context, the Hudson River Trading interview process typically includes a recruiter screen, one or two technical phone screens, and a 4-5 round on-site loop covering coding, system design (at L4+ levels), and behavioral. Reports tagged on LeakCode show the round-by-round distribution and typical difficulty calibration. To browse questions filtered by round type and seniority, use the company hub linked above.

How To Practice This Type of Question

Solve similar problems on LeetCode under timed conditions (25-35 minutes per medium difficulty). The goal is pattern recognition: recognize the underlying technique (sliding window, two-pointer, BFS, memoized recursion, etc.) within 60-90 seconds of reading. Strong candidates verbalize their hypothesis out loud before coding, then iterate based on feedback. Weak candidates dive into implementation immediately, lose time on the wrong approach, and run out of time for follow-ups.

Companies update their question pools every 2-4 months. The exact wording of any given question may have been retired by the time you interview. Focus your prep on the pattern, not the specific problem. The patterns that appear in Hudson River Trading reports consistently are the ones worth investing in; one-off niche problems are not.

During Your Hudson River Trading Round

Apply the standard interview round template: clarify requirements (2-3 minutes), state your approach out loud and confirm direction with the interviewer (3-5 minutes), code with narration (15-25 minutes), test with concrete examples including edge cases (5 minutes), discuss optimization or trade-offs if time permits (5 minutes). This template is universally accepted across FAANG and adjacent companies; deviating from it produces weaker interviewer feedback signal.

The single most predictive failure mode in Hudson River Trading reports tagged "no hire": not asking clarifying questions. Interviewers are explicitly trained to weight this. Strong candidates ask 3-5 clarifying questions even on problems that look obvious; weak candidates dive into code immediately. The clarifying-question check is often the first signal recorded in the interviewer's written notes.