Interview Question for Software Engineering Summer Intern at Facebook:

Mar 30, 2010

We can do it in seven races, we'll call them races A-F. For notation, we'll say that the Nth horse in race X is called X.N.

Races A-E: Divide the horses into 5 groups of 5 each such that each horse races only once.

We can eliminate the slowest 2 horses in each of the five races because there are definitely 3 horses faster in each case. As a result, we eliminate 5x2 = 10 horses: {A.4,A.5,B.4,B.5,C.4,C.5,D.4,D.5,E.4,E.5}

Race F: Race the fastest horses in each race A-E: {A.1, B.1, C.1, D.1, E.1}. To simplify notation, we'll label F.1 as horse A.1, F.2 as horse B.1, and so forth. That means the winner of this race is A.1, and it is the fastest horse of all. We don't have to race A.1 anymore.

We can eliminate D.1 and E.1 = 2 horses. Because they are not in the top 3.

As a result, we know that all remaining horses from D and E are eliminated. This is D.2,D.3,E.2,E.3 = 4 horses.

We know that A.1,B.1, and B.2 are all faster than B.3 (and similar for C.3) so they are not in the top 3.We can eliminate B.3 and C.3 = 2 horses.

Finally, we know that A.1 is faster than B.1, which is faster than C.1, and thus C.2, so we can remove C.2 = 1 horse.

Race G: We have removed 19 horses from competition and are sure that A.1 is the fastest horse of them all. This leaves just 5 horses: {A.2,A.3,B.1,B.2,C.1}. We race them and select the top 2 to join A.1 as the top 3 fastest horses.

just run them all on the one track :)
one race, and you get your 3 fastest horses in one go........or am I missing something!

6 races.

Divide 25 horses into 5 groups. Each group races and the fastest is selected.

The winner of each of the 5 races all race together. Pick Top 1,2 and 3.

My only concern: Could the answer be this simple?

B, you're mistaken. Imagine the top three fastest horses are Santa's Little Helper, Yojimbo, and I'm Number One. By random luck, in your first race, the five random horses you choose includes all three of those. I'm Number One wins and goes on to the final race; the other two do not.

8
5 top horses from each race of 5 races (25 / 5)
5 top contenders race; 1 wins--that's one top horse (5-1)
4 remaining top horses race, one wins; that's 2 top horses (4-1)
3 remaining top horses contend; winner is #3
That's 3 top horses from 8 races

Race#1 Race#2 Race#3 Race#4 Race#5
A1 B1 C1 D1 E1
A2 B2 C2 D2 E2
A3 B3 C3 D3 E3
A4 B4 C4 D4 E4
A5 B5 C5 D5 E5

Race#6
A1 B1 C1 D1 E1
Let's Say ranking
1st 2nd 3rd 4th 5th

Eliminate
            D1 E1
            D2 E2
            D3 E3
A4 B4 C4 D4 E4
A5 B5 C5 D5 E5

Left with
    B1 C1
A2 B2 C2
A3 B3 C3

Eliminate C3 as there are more than three faster horses C2, C1, B1, A1
Eliminate C2 as there are three faster horses C1, B1, A1
Eliminate B3 as there are three faster horses B2, B1, A1

Left with 5 horses for Race#7
    B1 C1
A2 B2
A3

So 7 races