This classic logic puzzle asks:

With 25 horses and a track that can race at most 5 at a time, what is the minimum number of races required to identify the top 3 fastest horses, knowing only the rank order of each race?

Constraints

  • No stopwatch; only relative order matters.
  • Each horse has a distinct but fixed speed.
  • Goal: Identify exactly the top 3 fastest horses.
  • Races are limited to 5 horses at a time.

Step-by-Step Strategy

Step 1: Group and Race

Divide the 25 horses into 5 groups of 5.
Race each group once → 5 races

Label horses by group and placement. Suppose the groups and results are:

  • Race A: A1, A2, A3, A4, A5 (A1 fastest)
  • Race B: B1, B2, B3, B4, B5
  • Race C: C1, C2, C3, C4, C5
  • Race D: D1, D2, D3, D4, D5
  • Race E: E1, E2, E3, E4, E5

Step 2: Race Winners

Now race the winners of each group: A1, B1, C1, D1, E1 → 1 race

Let’s assume result is: Race F: A1 > B1 > C1 > D1 > E1

This tells us:

  • A1 is the fastest horse overall
  • B1 and C1 are possible candidates for 2nd and 3rd

So far: 6 races

Step 3: Eliminate Horses

From the race results, we can now eliminate many horses:

  • Any horse slower than C1 is out of top 3.
  • Also, any horse not from the groups A, B, or C is out (since D1 and E1 lost to top 3 candidates).

From the remaining:

  • A1 (fastest)
  • B1, B2
  • C1, C2, C3
  • A2, A3

Candidates for 2nd and 3rd place are among these 5 horses:
A2, A3, B1, B2, C1, C2, C3
But A1 is already declared fastest.

Pick A2, A3, B1, B2, C1 to race → 7th race

Step 4: Final Determination

Race these 5 horses and take the top 2 finishers—those are the 2nd and 3rd fastest horses overall, since A1 is already the fastest.

Final Answer

Minimum number of races: 7

  • 5 initial group races
  • 1 race of the group winners
  • 1 final race among the refined candidates

Reference

  • [1] [Puzzle 9 (Find the fastest 3 horses)](https://www.geeksforgeeks.org/puzzle-9-find-the-fastest-3-horses/)