A logic problem by Vibha Sharma

Logic Level 3

"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?"


The answer is 7.

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1 solution

Vibha Sharma
Mar 11, 2016

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

     x2            x3

x6 x7

x11

so next race is btw these five horse

so total races = 7

very nice and logical solution

Laura Gao - 3 years, 3 months ago

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