CareerCup

6 trials for fastest horse and 7 for second fastest

Lets say we segregate the horses in 5 groups - A, B, C, D and E. We conduct 5 races and we get the winners in each of the category. Let them be A1, B1, C1, D1, E1.

Now we conduct a race between the first horses from each of the 5 categories. The winner is the fastest.

To find the second fastest, we need to see which are all the eligible ones. Lets work on an elimination concept for this. The horses that could come second are - B1, A2, A3.

We eliminate C1,C2.., D1, D2.. E1, E2.. etc because B1 is faster than C1 and C1 is faster than C2, C3 etc. Similar concept applied to groups D and E.

The race among B1, A2, A3 would give the second fastest horse.

Total number of races = 7

Can be done in only 4 races ....

Race [1]
Make 5 hourses run from one direction and another 5 from another direction, and also mark the middle point of the race...
Notice first 3 intersections of the hourses and select the hourses who crossed their first half mark as the 3 fastest...
Race [2] repeat this with another 10 hourses

Now we have 6 best hourses and 5 untested
Race [3] Make 4 hourses run from each direction and choose the 3 same as above
Now we have left with 6 hourses
Race [4] Make 3 hourses from each side run and choose the best 3....
Done in 4 races

@Sriram : Your first concern was actually valid. Your second comment is invalid because you cant note down the second fastest as you are not given a stopwatch.

I think of it as as function getMax with 5 parameters
function getMax(Horse []horse) // takes 5 horse parameters
{
//returns fastest horse
}

1. Creat 5 groups
2. call function 5 times for each 5 horse group
3. you have 5 fastest horse now
4. call function again with this 5 horses
5. you have the fastest horse now (total calls 5)
6. eliminate fastest horse and call function again with rest of 4 horses
7. you get the second fastest (total calls 5+1=6)

yups 7 is the answer

Let {A1,B1,C1,D1,E1} be the winners of 5 groups {A,B,C,D,E}
and {A2,B2,C2,D2,E2} be the runner ups of 5 groups
This would take 5 races
6th race among {A1,B1,C1,D1,E1} would give us the fastest horse.
Let C1 be the runner up in this race.
Now the eligible candidates for runner up position are {A2,B2,C2,D2,E2} and C1 as well
We conduct 7th race between {A2,B2,C2,D2,E2}
Let D2 be the winner of 7th race
Now we make C1 and D2 run in 8th race.
The winner of 8th race is the 2nd fastest of all.

Please suggest if there is any other better alternate...

Adding to this: It is possible to find the top 3 horses in 7 rounds itself.

Ans-7
Divide the horses into 5 groups(A,B,C,D,E).Now find the fastest and second fastest in each group(A1,A2,B1,B2,C1,C2,D1,D2,E1,E2).Now find the fastest among all by the race among top 5 fastest(A1,B1,C1,D1,E1).We can get the fastest from here.Now for the second
fastest conduct a race between the winner's group 2nd fastest and all other group fastest.winner of this race would be the second fastest horse.
like-suppose winner is C1 the conduct a race between A1,B1,C2,D1,E1.so winner of this race is second fastest.

yes its 7
Get the fastest in 6 races, that's clear. Also record the 2nd of each race. Now for 2nd fastest just race the 2nd from the 6th race with the 2nd from the group containing the fastest horse, that should do it.

7 Trials is the correct answer I guess!
*Split the 25 horses into 5 groups a,b,c,d,e.
*Note down the top 2 positions in each group. Let them be a1,a2,b1,b2 etc.
*Now we know that the fastest horse is one of these <a1,b1,c1,d1,e1>
*To find the second fastest. Pick the second fastest horse from the group, from which the first horse was picked. i.e
- If a1 was picked then pick a2. If b1 then b2
*Now test this horse against the fastest horses of the other groups. i.e if a1 was picked then conduct a race between a2,b1,c1,d1 and e1. Else if b1 was picked then conduct a race between a1,b2,c1,d1 and e1

there may be chance b1>a2 , then it will be more rounds right?

This is my solution : 8 Rounds
I will split 25 horses into 5 groups, each group having 5 horses. For each group, i will track 1st and 2nd fastest horses. This will take 5 rounds.

I will arrange a race for first fastest horses in the 6th round. I get the fastest horse among all 25 horses. But i will track the second fastest horse in this round as well.

In 7th round, there will be a race of all second fastest horses. I will track the fastest horse here.

In 8th round, there will be a race between 6th second fastest and 7th fastest horse. Fastest horse here would be the second fastest among all the 25 horses.

8 is the correct answer...7 is wrong