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Find 3 Fastest horses from 25 hourses

 

There are 25 horses. We have to find out the fastest 3 horses. In one race maximum 5 horses can run. How many such races are required in minimum to get the result ?

find 3 fastest horses from 25 horses puzzle

CHECK BELOW FOR ANSWER IF U CANT SOLVE IT

We can first do 5 races by taking 5-5 horses and get top horse in each race
Lets say it looks like this
O1,O2,O3,O4,O5
T1,T2,T3,T4,T5
TH1,TH2,TH3,TH4,TH5
F1,F2,F3,F4,F5
FV1,FV2,FV3,FV4,FV5
Here O1 > O2 > O3 > O4 > O5 same way for others.
Now lets take fastest horse in each race and then have one race between them, so have race in O1, T1, TH1, F1 and FV1.
Lets say O1, TH1 and F1 comes in top three(and O1 > TH1 > F1), then there are no chances that horses slower than T1 and FV1 can come in top 3 and we can also say that O1 is fastest horse and also F2-F5 horses are not among top 3.
Now we need to find second and third fastest horses
they can be from O2,O3,TH1,TH2 and F1, So we will have once more race among them to determine second and third position.
Thus a total of minimum 7 races are needed to find top 3 horses from 25 horses.