The 3 Fastest Horses
The Puzzle: You have 25 horses and a track that can only race 5 horses at a time. What is the minimum number of races needed to find the Top 3 fastest horses? (You don’t have a stopwatch).
1. The Strategy
Step 1: Initial Grouping (5 Races)
Divide 25 horses into 5 groups (A, B, C, D, E) and race each group.
- We get the winners of each group: A1, B1, C1, D1, E1.
Step 2: The Winner of Winners (1 Race)
Race the 5 group winners: A1, B1, C1, D1, E1.
- Let’s assume the result is: A1 > B1 > C1 > D1 > E1.
- Result: A1 is the absolute fastest (1st place).
Step 3: Eliminating the Impossible
Who could be 2nd or 3rd?
- From Group A: A2 or A3 (since A1 is 1st).
- From Group B: B1 or B2 (B1 lost to A1, so it could be 2nd. B2 could then be 3rd).
- From Group C: Only C1 (It lost to A1 and B1, so the best it can be is 3rd).
- D and E: Entirely eliminated. D1 is 4th at best.
Step 4: The Final Race (1 Race)
We have 5 candidates left: A2, A3, B1, B2, C1.
- Race these 5. The top two from this race are the 2nd and 3rd fastest overall.
Interview-Focused Questions
Q: What is the total number of races?
A: 7 races. (5 group races + 1 winner’s race + 1 final heat).
Q: Why is A3 included but B3 is not?
A: If A1, A2, and A3 were the three fastest horses in the whole set, they would have been in the same group. Since A1 is the fastest overall, A2 and A3 are still “untested” against the other group winners. B3 cannot be top 3 because B1 and B2 are already faster, and A1 is also faster.
Q: How does the answer change if you have a stopwatch?
A: If you have a stopwatch, you only need 5 races. You just record the times of all 25 horses and pick the 3 smallest.
Key Takeaway
This puzzle tests your ability to prune a search space. Most people fail because they try to race too many horses in the final step.
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