Rank the horses!
Out of 25 horses you have to find the overall 1st, 2nd and 3rd fastest horses. Maximum 5 horses are allowed per race. What is the minimum number of races required? Note: You are not allowed to time the horses. You can only note the positions of every horse in the race compared to the other horses in that race only.
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1 solution
First , we divide 25 horses into 5 groups. Then, we arrange 5 races for these 5 groups.
Second , we arrange 1 race (the 6th race) among the 5 group winners. The winner of this race is the fastest horse (Say, it's horse A).
Third , we take the horses who stood 2nd (Name it horse B) and 3rd (Name it C) in the 6th race. Then, we take the horses who stood 2nd (Call it horse D) and 3rd (Call it E) in horse A's initial group battle. We also take the horse who stood 2nd in horse B's initial group race. Finally, we arrange 1 race (the 7th race) among horses B, C, D, E and F. The winner of this race is the 2nd fastest horse while the runner up is the 3rd fastest.