I knew this one but still fumbled the explanation a bit.
Start by clarifying the problem constraints and then walk through a systematic elimination strategy. For the fastest horse, use 5 initial races to find the best of each group, then race those winners to identify the overall fastest. For the top 3, extend the logic by considering only horses that could possibly be in the top 3 based on race results, and use additional races to determine the final ranking.
Pro tip: Explicitly state your assumptions (e.g., no ties, consistent performance) and then explain how you would handle ties if they occur. This shows attention to detail and robustness, which is highly valued in engineering roles.
Confirm that there are 25 horses, each race can have up to 5 horses, and we need the minimum number of races to find the fastest (and top 3). Assume no ties and that horse performance is consistent.
Divide the 25 horses into 5 groups of 5. Race each group (5 races). Then race the 5 winners (1 race). The winner of this race is the fastest overall. Total: 6 races.
After the 6 races, label groups A-E by the rank of their winner in the winners' race. The fastest horse is A1. Potential top 3 horses are limited: A2, A3, B1, B2, C1. All others are eliminated.
Race the 5 candidate horses: A2, A3, B1, B2, C1. The top two from this race, along with A1, are the top 3 overall. Total races: 7.
Confirm that 7 is minimal by arguing that at least 5 races are needed to see all horses, and additional races are required to compare winners and resolve the top 3. Mention that if only the fastest is needed, 6 races suffice.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.