25 Horses Problem-Solution
Divide the set of 25 horses into 5 non-overlapping sets of 5
horses each. Have a race each for all the horses in each
set. This makes it a total of 5 races, one for each set.
Now, have a race for the winners of each of the previous 5
races. This makes it a total of 6 races.
Observe the position of each horse in the 6th race and
correspondingly number the sets. i.e. the set of the winner
of 6th race will be said to be set no. 1 while the set of
the loser of the 6th race will be said to be set no. 5.
Now, possible candidates for the first three positions
exclude the followings:
1. Any horse from set 4 or set 5.
2. Any horse except the winner from set 3,.
3. Any horse except the winner and the 2nd position from set 2.
4. Any horse except the winner, 2nd position and 3rd
position from set 1.
So now we have 6 candidates for top 3 positions. However, we
know that the winner of set 1 is the fastest horse in the
whole group of 25 sets.
So now we have 5 candidates for the second and third
position. What better way to find out who’s who than to have
a race of these 5 horses. Race them and this will solve our
problem in just 7 races.