50 Challenging Problems in Probability [Part 16]: Will Second-Best Be Runner-Up?

<h2>Solution:</h2> <p>To ensure that the second-best player wins the runner-up cup, they must be placed in a different half of the ladder from the best player. This means that if the best player’s starting number (for the first round) is between 1–4, then the second-best player’s starting number has to be between 5–8. Similarly, if the best player’s starting number is between 5–8, then the second-best player’s starting number has to be between 1–4.</p> <p>The total number of rungs not occupied by the best player is 7 (since the best player can only occupy one rung). The total number of rungs the second-best player can occupy to win the runner-up is 4 (which represents the other half of the ladder from the best player).</p> <p><a href="https://medium.com/@shelvia1039/50-challenging-problems-in-probability-part-16-will-second-best-be-runner-up-9c041f108fd7"><strong>Website</strong></a></p>