Racing! The 25 Horses Puzzle. The Solution.

You have 25 horses. One track. No stopwatch!

You need to find the fastest 3 horses. But it costs $1,000 a race to hire the track!!!

What’s the fewest races in which you can determine the fastest three horses?

First up let’s race all 25 horses, by having 5 races of 5 horses each.

Call these races A, B , C, D and E. And the winning horses W_A , W_B , W_C , W_D and W_E.

Now run a 6th race featuring the 5 horses that each won a race.

Say these 5 horses race and finish in the order W_B , W_A , W_D , W_C and W_E.

At this stage we can start to cull the field. We can remove all the horses in race C and E because W_B , W_A , and W_D are faster than all ten of them.

We can also remove the slowest two horses in race B, because they finished 4th and 5th in a race.

The slowest three horses in race A finished behind the winner and second place in race A, AND we know that W_B is faster than W_A , so all three of them can go.

Finally W_B and W_A are both faster than W_D . So all the horses in race D, except W_D , can also go.

Removing all those horses we are left with W_B which we know is the fastest horse of all, and 5 other horses.

Have a 7th race featuring those 5 horses.

Our fastest 3 horses are W_B and the fastest two horses from this 7th race.

It takes 7 races to pick the fastest three horses.