Friday 15 April 2016
Logical Qn : Assume 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?
After analyzing a bit, Here are the pointers.
- We need to put all the horses into a race ( 5 at a time ) to find out the best 3 performers.
- Maximum 5 Horses in a race, so 5 times we need to conduct.
- After 5 Races, below is the table we can draw "ORDER by best performer"
Race1H1 - Race2H6 - Race3H11 - Race4H16 - Race5H21
Race1H2 - Race2H7 - Race3H12 - Race4H17 - Race5H22
Race1H3 - Race2H8 - Race3H13 - Race4H18 - Race5H23
Race1H4 - Race2H9 - Race3H14 - Race4H19 - Race5H24
Race1H5 - Race2H10 -Race3H15 - Race4H20 - Race5H25
Our Aim is to find the best three performers. so, we can eliminate last two rows.
Reason: We are least bothered about 4th and 5th best in each race.
They can not be one among top three performers.
Our Target table is
Race1H1 - Race2H6 - Race3H11 - Race4H16 - Race5H21
Race1H2 - Race2H7 - Race3H12 - Race4H17 - Race5H22
Race1H3 - Race2H8 - Race3H13 - Race4H18 - Race5H23
Now Race # 6: all top players in each race:
i.e
Race1H1 - Race2H6 - Race3H11 - Race4H16 - Race5H21
Assume results are, 1st place Race1H1 ; 2nd place Race2H6 ; 3rd place Race3H11
Now Race # 7: will gives the 2nd and 3rd place horse.
i.e we need to conduct a race with below set.
- Race2H6 - Race3H11
Race1H2 - Race2H7
Race1H3
why we eliminated other horses?
Elimination Set # 1
Race4H16 - Race5H21
Race4H17 - Race5H22
Race4H18 - Race5H23
Reason: As 3rd best horse is Race3H11. so, above set is definitely is not in 1,2,3 positions.
Elimination Set # 2
Race3H12
Race3H13
Reason: same as above.
Elimination Set # 3
Race2H8
Reason: as Race1H1 is 1st , there may be chance for 2nd is Race1H2 or Race2H6
chance for 3rd is Race1H3, Race2H6, Race2H7, Race3H11
but not Race2H8
so, Answer is 7
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