satishchandra wrote:On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number of races we need to conduct to get the top 3 fastest horses?
A. 5
B. 7
C. 8
D. 10
E. 11
Easier to see with a concrete example.
Round 1: 5 races, with the horses in descending order:
A-B-C-D-E
F-G-H-I-J
K-L-M-N-O
P-Q-R-S-T
U-V-W-X-Y
Winners are A, F, K, P, and U.
Round 2: 6th race, with the horses in descending order:
A-F-K-P-U.
The fastest horse of all is A.
F is faster than K.
Thus, if K is among the 3 fastest, then the 3 fastest will be A-F-K.
Thus, none of the horses L-Y can be among the 3 fastest.
But there are several horses against whom F and K still haven't raced.
F:
F still needs to race against B and C, who were top-3 finishers in Round 1, and could be faster than F.
K:
K still needs to race against B and C, who were top-3 finishers in Round 1, and could be faster than K.
K also has not yet raced against G or H, who also were top-3 finishers in Round 1.
But if G is among the 3 fastest horses, then the 3 fastest will be A-F-G, implying that H cannot be among the 3 fastest.
Thus, K still needs to race against G but not against H.
Round 3:
1 more race with F, K, B, C, and G.
Total number of races needed = 7.
The correct answer is
B.
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