Races To Find Horses For Courses
What was the task?
First we need to make 5 groups of 5 horses each. Let's put each group on race & note down rank of each horse & corresponding group. This requires 5 races.
Taking out winner of each group aside. In a next race, winner of each group run & fastest winner is found. Total 6 races are conducted till now.
Now let's name group of fastest winner as A, second fastest winner as B & so on as C, D, E. Each horse would be identified by it's group name & rank as Group.Rank. For example, B.3 means the horse that came 3rd in group B & D.5 is horse that came last in group D.
For next race, we can eliminate few. Let's remind we have to find 3 fastest horses. Now let's logically eliminate few horses. Those horse for which we are sure that at least other 3 are faster than those will be eliminated.
1. Now A.1, B.1 & C.1 are faster than D.1 & E.1. So D.1 & E.1 & respective groups eliminated straightaway.
2. The C.2 (& other members of C) eliminated as A.1, B.1, C.1 are faster ones.
3. The B.3 (& other member of B) eliminated as at least A.1, B.1, B.2 are faster ones.
4. Similarly, A.4 & A.5 have 3 horses ahead as A.1, A.2 & A.3.
5. A.1 is already proved it's fastest among all, so no need to re race by taking it.