"Let's say that you have 25 horses, and you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time because there are only 5 tracks. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?"
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let x1 , x2 .......x25 are the horses
five races done and result is as follow
Fastest slowest
x1 x2 x3 x4 x5
x6 x7 x8 x9 x10
x11 x12 x13 x14 x15
x16 x17 x19 x20 x21
x22 x23 x24 x25 x26
no. of races = 5
now we require only 3 fast horse so remove the 4th and 5th horse from races and remaining are as follow
x1 x2 x3
x6 x7 x8
x11 x12 x13
x16 x17 x18
x21 x22 x23
now we 6th race is happen btw the fastest horse of the five races because we want to fin d fastest horse
x1 x6 x11 x16 x21
let x1 x6 x11 are 1st , 2nd and 3rd respectively
then reject x16 and x21 then x17 , x18 , x22 , x23 are automatically reject because they are slower than x16 and x21
now remaining horses are as follows
x1 x2 x3
x6 x7 x8
x11 x12 x13
x1 is the fastest among them because
x1 is faster than x2 and x3 in 1st race and faster than x11 and x12 in 6th race
so automatically faster than x7 , x8 and x12 , x13 because the are slower than x6 and x11 respectively
so first horse is x1 now we have to find 2 more horse
since x11 is at 3rd no in 6th race so we don't require horses slower than this so reject x12 and x13
similarly x6 is at 2nd no s x7 may be at third no so we don't require horses slower than x7 so reject x8 now remaining horses are
x6 x7
x11
so next race is btw these five horse
so total races = 7