25 Horses, 5 Lanes - Find Top 3 Fastest

Problem: 25 horses need to be raced on a track with only 5 lanes; there is no stopwatch, so only relative finishing order within each heat is known. Find the minimum number of races required to identify the top 3 fastest horses overall.

Constraints: Max 5 horses per race; only ranking (not timing) is available per race.

Example: Splitting the 25 horses into 5 groups of 5 gives 5 initial heats.

Approach: Run 5 heats (1 per group) to rank each group internally. Race the 5 group-winners against each other (6th race) to find the fastest horse overall and narrow down candidates for 2nd/3rd using group-relative standings. A 7th race between the remaining plausible candidates for 2nd and 3rd place resolves the final ranking. Total: 7 races.