Question:
There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race.
What will be the minimum no. of races which are required to get the top 3 horses.
Solution:
The solution is 7.
Make group of 5 horses and run 5 races. Suppose five groups are a,b,c,d,e and next alphabet is its individual rank in this group(of 5 horses).for eg. d3 means horse in group d and has rank 3rd in his group. [ 5 RACES DONE ]
a1 b1 c1 d1 e1
a2 b2 c2 d2 e2
a3 b3 c3 d3 e3
a4 b4 c4 d4 e4
a5 b5 c5 d5 e5Now make a race of (a1,b1,c1,d1,e1).[RACE 6 DONE] suppose result is a1>b1>c1>d1>e1
which implies a1 must be FIRST.
b1 and c1 MAY BE(but not must be) 2nd and 3rd.
FOR II position, horse will be either b1 or a2
(we have to find top 3 horse therefore we choose horses b1,b2,a2,a3,c1 do racing among them [RACE 7 DONE].
The only possibilities are :
c1 may be third
b1 may be second or third
b2 may be third
a2 may be second or third
a3 may be third
The final result will give ANSWER. suppose result is a2>a3>b1>c1>b2
then answer is a1,a2,a3,b1,c1.
HENCE ANSWER is 7 RACES
