25 horses
You have 25 horses and a track that races 5 at a time. There is no stopwatch: each race only tells you the finishing order of those 5. Horses always run at the same speed.
What is the fewest races needed to find the 3 fastest horses, in order?
Show hint
Start with 5 heats and one race of the heat winners. After that, which horses can still be in the top 3?
Show solution
7 races.
- Races 1 to 5: race every group of 5.
- Race 6: race the five group winners. The winner of this race is the fastest horse overall.
- Label the race 6 finishers A, B, C (1st to 3rd). Only five horses can still be 2nd or 3rd overall: A's group 2nd and 3rd place, B and B's group 2nd place, and C.
- Race 7: race those five. The top two are 2nd and 3rd overall.
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