25 Horses. When you race 5 horses, you know that any horse that doesn’t win isn’t the fastest. Every horse needs to be raced at least once, or you will have no idea how good it is. Each race rules 4 horses out of the running for fastest, so you need 6 races to find the fastest horse.
However you arrange it, you can’t guarantee that the best horse only runs once, so sometimes you will have 2 horses that only lost to the best. Either could be second.
There is no strategy that always finds the first and second in 6 races.
There is a strategy that always finds the best three in 7 races. 5 groups, winners race, those which were directly beaten by at most 2 horses race. (
There is a strategy that always finds the best three in a variable number of races that is sometimes as low as 6.
25 Horses. When you race 5 horses, you know that any horse that doesn’t win isn’t the fastest. Every horse needs to be raced at least once, or you will have no idea how good it is. Each race rules 4 horses out of the running for fastest, so you need 6 races to find the fastest horse.
However you arrange it, you can’t guarantee that the best horse only runs once, so sometimes you will have 2 horses that only lost to the best. Either could be second.
There is no strategy that always finds the first and second in 6 races.
There is a strategy that always finds the best three in 7 races. 5 groups, winners race, those which were directly beaten by at most 2 horses race. (
There is a strategy that always finds the best three in a variable number of races that is sometimes as low as 6.
I know the 7 races solution, but this proof that 6 doesn’t work is nice!