There are 25 horses and only five tracks in a race.
How do you find the second coming horse of all the 25
horses, provided there is no stop clock? (obviously, a
horse cannot participate more than once in a race).

Divide the set of 25 horses into 5 non-overlapping sets of 5
horses each. Have a race each for all the horses in each
set. This makes it a total of 5 races, one for each set.

Now, have a race for the winners of each of the previous 5
races. This makes it a total of 6 races.

Observe the position of each horse in the 6th race and
correspondingly number the sets. i.e. the set of the winner
of 6th race will be said to be set no. 1 while the set of
the loser of the 6th race will be said to be set no. 5.

Now, possible candidates for the first three positions
exclude the followings:
1. Any horse from set 4 or set 5.
2. Any horse except the winner from set 3,.
3. Any horse except the winner and the 2nd position from set 2.
4. Any horse except the winner, 2nd position and 3rd
position from set 1.

So now we have 6 candidates for top 3 positions. However, we
know that the winner of set 1 is the fastest horse in the
whole group of 25 sets.

So now we have 5 candidates for the second and third
position. What better way to find out who's who than to have
a race of these 5 horses. Race them and this will solve our
problem in just 7 races.

LAST TWO CAN BE REMOVED FROM EACH GROUPS.
WE HAVE LEFT WITH 9 HORSES.

6 RACE(F) A1->F1 B1->F5 C1->F2 D1->F3 E1->F4

SUPPOSE (CAN BE GENERIC,ANALYS) FROM RACE(F)

NOW F1(A1) IS FASTES HORSE AMONG 25.
ALL HORSES FROM GORUP B AND E CAN BE ELIMINATED(since E1
and B1 is at 4th and 5th position respectivly). AND ANALYS
A BIT, C3, D2 AND D3 ALSO CAN BE ELIMINATED (since in any
senario C3 will max come 4th, D2->4th and D3->5th). NOW
LEFT WITH 5 HORSES.

5X5 = 25...
make group of 5 and total 5 such groups ...
race each grup at a time... select winner from each group.
race these 5 winners ... and mark them as their positions

best case: the fastest horse and the 2nd coming horse are
in two different group. Then we can simply say the 2nd
coming horse in the winners' race is the answer.

worst case: the fastest horse and the 2nd coming horse are
in same group. So any from the four except the winner from
the fastest horse's group (say 1st group) may be the 2nd
coming horse.

so need another race.... 4 from 1st group (except winner)
and winner of 2nd group .... who wins is 2nd best.

I was asked this question in microsoft.
The correct answer to find out top 3 horses is 7.
Explaination of Desinerd i.e. Answer#1 seems the most
appropriate.

Run each horse in a race, always keeping the top two to
compete in the next race, until the last race in which the
top two are identified. So run 8 races instead of 7,
sometimes the simple solution is the best.

Obviously a horse can't run twice in a race. Sometimes when
something is too obvious it makes you think it's a trick
statement.

The first soln is correct, but I think its not understandable.
and @ Animesh Sonkar, your soln is correct until 6th race.
In the 7th race, u have eliminated the first rank, the fouth
nd the fifth. But u have raced only 4 horses.. that is whr u
missed. Correct Soln.:-

The fifth horse in the seventh race would be rank 2 horse of
the group which has 2nd rank in the fifth (all winners) race.
So, all the scenarios would be taken care of now.

Eg. after 5th race, let the positions be:

A1 B1 C1 D1 E1 (in order of rank)

now A1 is the fastest.--> eliminate it
D1 nd E1 can't be 2nd nd 3rd.(!!!)
Now we remain with B1 nd C1.

The other horses in the race would be A2 A3 and B2.

So, in every possible case, we can get the first three
positions confirmed.
* We don't need B3 because, B1 nd B2 are already faster than
it (evn after leaving A1), therefore, it can't be 3rd.

* We don't need horse C2 because, B1 nd C1 are already
faster than C2, therefore it is not the contender of top
three positions.

Obviously horses must be allowed to compete in more than one
race, and they are assumed not to tire as they run races, so
their performance is constant.

Round 1: 5 races of 5
Round 2: 5 winners of Round 1
-> winner is overall 1st place (6 races)
Round 3: 2nd and 3rd places from Round 2,
plus horses that came 2nd & 3rd behind Round 2 1st
placer in
Round 1
plus horse that came 2nd behind Round 2 2nd placer in
Round 1
-> winner is 2nd place overall
-> 2nd place is 3rd place overall

So you can find the winner in 6 races (trivial) and top
three in 7 races.

You cannot simply take the fastest horse from each group of
five. You have to look at the times of all the horses and
take the five fastest times from all 25 and then select the
top 5. Some would argue length and turf play in, but all
else equal, the fastest horse of one race could be slower
than the slowest of the other 4 races, so the winner of
each race is not a good answer.

What is the minimum number of numbers needed to form every
number from 1 to 7,000?
Example: To form 4884, you would need 2 4s & 2 8s. 4822
requires a 4, a 8, & 2 2s, but you would not count the
numbers again that you had already counted from making 4884.

A number of 9 digits has the following properties:
? The number comprising the leftmost two digits is
divisible by 2, that comprising the leftmost three digits
is divisible by 3, the leftmost four by 4, the leftmost
five by 5, and so on for the nine digits of the number i.e.
the number formed from the first n digits is divisible by
n, 2<=n<=9.
? Each digit in the number is different i.e. no
digits are repeated.
? The digit 0 does not occur in the number i.e. it is
comprised only of the digits 1-9 in some order.
Find the number.

A soldier looses his way in a thick jungle. At random he
walks from his camp but mathematically in an interesting
fashion.
First he walks one mile East then half mile to North. Then
1/4 mile to West, then 1/8 mile to South and so on making a
loop.
Finally how far he is from his camp and in which direction?

Last Saturday Milan went for the late night show and came
late. In the morning family members asked him which movie
did he see. He gave different answers to everyone.
? He told to his father that he had gone to see MONEY.
? According to his mom, he saw either JOHNY or BABLU.
? His elder brother came to know that he saw BHABI.
? To his sister, he told ROBOT.
? And his grandpa heard that he saw BUNNY.
Thus, Milan gave six movie names, all five letter words. But
he saw some other movie with five letter word. Moreover,
each of the six movie names mentioned above has exactly two
letters common with the movie he saw. (with the same positions)
Can you tell which movie did Milan see?

Six cabins numbered 1-6 consecutively, are arranged in a row
and are separated by thin dividers. These cabins must be
assigned to six staff members based on following facts.
1. Miss Shalaka's work requires her to speak on the phone
frequently throughout the day.
2. Miss Shudha prefers cabin number 5 as 5 is her lucky number.
3. Mr. Shaan and Mr. Sharma often talk to each other during
their work and prefers to have adjacent cabins.
4. Mr. Sinha, Mr. Shaan and Mr. Solanki all smoke. Miss
Shudha is allergic to smoke and must have non-smokers
adjacent to her.
5. Mr. Solanki needs silence during work.
Can you tell the cabin numbers of each of them?

John lives in "Friends Society" where all the houses are in
a row and are numbered sequentially starting from 1. His
house number is 109.
Jessy lives in the same society. All the house numbers on
the left side of Jessy's house add up exactly the same as
all the house numbers on the right side of her house.
What is the number of Jessy's house? Find the minimal
possible answer.