25 Horses Puzzle

25 horses are there...and u have a Race Course with 5 lanes in it......how many minimum no of races u'll have to do in order to find 1,2 and 3?

group into 5 groups,conduct 5 races.(5 races)
take the best from each group conduct one more race.(6TH Race)

by this we have surely got the best horse(1st).
but the problem is about 2nd,they can be from 2 possible different groups.
similarly 3rd horse can be from 3 different groups.

so take the 2 horses from the same group as the top horse.
take best and second best from the group the which contributed the second best horse in 6th race.
take the horse that came 3rd in the 6th race.

now conduct a race between these 5.
they will decide 2nd and 3rd best horses.(remember top is already chosen).


example:
let the groups be A,B,C,D,E.
A(i) represents the horse that came in ith position in the race within the group.

suppose A(1),B(1),C(1) came 1st,2nd and 3rd resp. in the sixth race.
7th race should be between
A(2),A(3),B(1),B(2),C(1)

hence 7 races are enough to decide top 3 among 25 horses.

--solution by beagle(ankit garg)