Race to 50

What this game-theory interview question tests

This is a medium-difficulty combinatorial game theory problem, popular at quantitative firms because it rewards backward induction and strategic thinking over computation. The question asks you to find a winning opening move in a turn-based game where both players play optimally.

To solve problems like this, work backwards from the goal state. Identify which positions are winning (where the player to move can force a win) and which are losing (where the opponent can force a win no matter what you do). Once you map the game tree, your first move should put your opponent in a losing position. The key insight is recognizing that certain sums leave your opponent with no good options, regardless of their choice from the allowed range.

• Backward induction and game-state analysis
• Winning and losing positions
• Strategies that eliminate opponent options