You have 25 horses. You can race 5 at a time. What is minimum number of races to find the fastest 3?

You have 25 horses. You can race 5 at a time. What is minimum number of races to find the fastest 3?

Approach: Use tournament elimination.

7 races. First 5 races (groups of 5). Then race winners (6th race). Keep fastest horse's group, 2nd fastest's group, 3rd fastest's group. 7th race: 2nd and 3rd from fastest's group, 2nd from 2nd's group, and 1st and 2nd from 3rd's group.

Follow-up: What about fastest k horses?

Key concepts: tournament, elimination, optimal strategy.