Clashing pirates

What this hard probability question tests

This is a hard probability problem that combines circular symmetry, conditional elimination, and strategic reasoning about sequential events. Quant firms use problems like this to assess whether a candidate can track state-space evolution when outcomes depend on both randomness and deterministic rules.

The core challenge is that each round eliminates exactly one pirate based on a random selection and a fixed comparison rule, and you must reason about which configurations survive to the final round. Success requires setting up the dependency structure carefully, avoiding the temptation to oversimplify, and tracking which initial arrangements and sequence of events lead to your target outcome.

• Conditional probability and sequential filtering
• Symmetry and counting under constraints
• Deterministic outcomes within a random process
• State-space reduction across rounds