Sheep vs 100 Tigers Survival

This puzzle describes a population of predators and a single prey on an isolated island, where predators can also survive on an alternative food source. The twist is that any predator who eats the prey changes type and becomes prey themselves, while the others retain their original incentives and full knowledge of the rules. Candidates must reason about whether anyone will choose to attack, knowing that doing so changes the future configuration of the island and the balance of risk. The problem is a classic brain teaser found in quantitative trading and research interviews to test abstract strategic reasoning.

Solving it leans heavily on backward induction and pattern recognition across different population sizes. The interviewer expects the candidate to strip away the large numbers, analyze very small cases carefully, and then generalize by induction. Recognizing that an invariant related to parity drives the strategic outcome is central. Strong answers clearly state assumptions about rationality, show consistent recursive logic, and explain why no individual tiger would deviate from the predicted behavior once the pattern is identified.

What it tests

This class of problems is governed by backward induction and parity analysis in sequential decision-making with perfect information. The key structure is that each agent's optimal move depends on predicting the consequences of their action, assuming all others are equally rational and will act to maximize their own survival. The recursive logic means that the outcome for $n$ agents depends directly on the outcome for $n-1$ agents, creating a chain of reasoning that can be unwound from the simplest cases. Parity (odd/even) becomes crucial because it determines whether taking the risky action (eating the sheep) leaves you in a safe or unsafe position in the next round. This pattern holds because each agent's risk is not just immediate, but also a function of how many future threats remain after their action, and parity is the simplest invariant that tracks this across steps.