Determine the Top Three Horses

Solution & Explanation

To determine the top three fastest horses out of 25 with a racetrack that accommodates only 5 horses at a time, we can follow a systematic approach, ensuring we minimize the number of races required. The solution involves a total of 7 races, explained as follows:

Step-by-Step Explanation

1. Initial Grouping and Racing:

   • Divide the 25 horses into 5 groups of 5 horses each. Label these groups as A, B, C, D, and E.
   • Conduct 5 races (one for each group) to determine the fastest horse in each group. After these races, you will have 5 winners: A1, B1, C1, D1, and E1. This step takes a total of 5 races.

2. Race the Winners:

   • Conduct a race with the 5 winners from the initial group races (A1, B1, C1, D1, E1) to determine the fastest horse overall. Let's assume the result is: A1 > B1 > C1 > D1 > E1. This step takes 1 race.
   • At this point, A1 is identified as the fastest horse overall.

3. Determine the 2nd and 3rd Fastest Horses:

   • Select the relevant candidates for the final race to determine the 2nd and 3rd fastest horses:
     • From Group A (the group of the fastest horse A1), choose A2 and A3 (the 2nd and 3rd place horses in Group A).
     • From Group B (since B1 was the 2nd fastest in the winners' race), choose B1 and B2 (the 1st and 2nd place horses in Group B).
     • From Group C (since C1 was the 3rd fastest in the winners' race), choose C1 (the 1st place horse in Group C).
   • Conduct a final race with these 5 horses: A2, A3, B1, B2, and C1.
   • The top two horses from this race will be the 2nd and 3rd fastest overall.

4. Conclusion:

   • The total number of races conducted is 7 (5 initial races + 1 winners' race + 1 final race for 2nd and 3rd place).
   • This method ensures that we efficiently determine the top three fastest horses with the minimum number of races possible, considering the constraints of the racetrack and the information available after each race.