A logic problem by Payal Sheth
There are 25 horses. You have to get first 3 fastest horses out of all 25 by making some number of matches between them.
Rule 1: You have no gadget to count the time taken.
Rule 2: Only 5 horses can run on the track (ground) at one time.
What is the minimum number of matches you will have to conduct to choose these 3 fastest horses?
Hint 1 : Try and eliminate as many horses as possible.
Hint 2 : The horse which comes 2nd in one match can be possibly faster than the winner of 2nd match (when you divide the horses in groups of 5 and arrange matches.)
The answer is 7.
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1 solution
Arrange 5 matches of the horses. Now eliminate the 4th and 5th rank horses from each as they can't be among the top 3 fastest horses.
Take the winners of all the matches and arrange the 6th match among them. The horse which comes 1st in this match is the fastest among all 25 horses. Eliminate the 2 horses which came 4th and 5th in this match, as they too can't be among top 3 again. now, as they were the winners of some match, the horses which came 2nd and 3rd in that respective matches should be also eliminated as they are slower than these 2. now we remain with 9 horses. Now look at the horse which came 3rd in the race of toppers of all matches. He can be minimum at the 3rd place as we already have the fastest horse and one more horse, as we know, is faster than this one. Thus, eliminate the 2nd and 3rd rank horse from this one's line (this can be minimum 3rd and thus the ones slower than him should be eliminated.) Similarly eliminate rank 3 horse from the row of rank 2 horse as his minimum rank can be 4.
Now, we are left with 6 horses, from which we know the rank 1 horse. Arrange the 7th match between the remaining 5, and we will get the rank 22 and rank 3 horses.
Thus we get the top 3 fastest horses in 7 matches by just eliminating the ones which cannot stand in the match for first 3 ranks by logic.