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25 horses, 5 tracks & 3 fastest horses puzzle
- Given 25 horses and a racing track.
- 5 horses can run simultaneously on a racing track.
- We want to find 3 fastest horses among 25 horses.
- Find the minimum number of races required to find 3 fastest horses.
Solution of 25 horses, 5 tracks & 3 fastest horses puzzle
- Let us first organize the horses in five groups and each group having five horses.
- We will carried out five races among the groups and results are as shown in Table 1
Table 1 : Races of five groups
Group | Horses |
Race Result |
Top 3 horses |
1 | H1, H2, H3, H4, H5 |
H1, H2, H3, H4, H5 |
H1, H2, H3 |
2 | H6, H7, H8, H9, H10 |
H6, H7, H8, H9, H10 |
H6, H7, H8 |
3 | H11, H12, H13, H14, H15 |
H11, H12, H13, H14, H15 |
H11, H12, H13 |
4 | H16, H17, H18, H19, H20 |
H16, H17, H18, H19, H20 |
H16, H17, H18 |
5 | H21, H22, H23, H24, H25 |
H21, H22, H23, H24, H25 |
H21, H22, H23 |
- We got five fastest horse among five groups.
- We will arrange 6th race among the winners.
- H1, H6, H11, H16, H21 and results are shown in Table 2.
Table 2 : Sixth Race result
Group | Horses |
Race Result |
Top 3 horses |
6 | H1, H6, H11, H16, H21 |
H1, H11, H21, H6, H16 |
H1, H11, H21 |
- Let us analyze the race result of Group 6 (Table 2)
- We got H1 as winner among the fastest horses of group 1 to 6. (Table 1 and 2)
- H1 is the fastest horse among 25 horses.
- Now, we will find horse for 2nd and 3rd place.
- H6 is fourth in group 6 Race.
- H6 can not be among top 3 fastest horses.
- We will eliminate H6 horse.
- H6 was winner in Group 2 race
- Group 2 horse are slower the H6 horse.
- We can eliminates all horses of group 2.
- H16 is fifth in group 6 Race.
- Similarly, we can eliminates group 4 horses.
- We have summarized results in Table 3
- We have eliminated group 2 and group 6 from table 1..
- We have shown Group 6 result (for reference).
- Now, We will perform the elimination from Table 3 as per last six races.
Table 3 : Outcome of 6 races
Group |
Horses |
Top 3 horses |
1 |
H1, H2, H3, H4, H5 |
H1, H2, H3 |
3 |
H11, H12, H13, H14, H15 |
H11, H12, H13 |
5 |
H21, H22, H23, H24, H25 |
H21, H22, H23 |
6 |
H1, H6, H11, H16, H21 |
H1, H11, H21 |
- H21 was third as a result of Group 6 result.
- In group 5, H22 and H23 can not be top 3 horse. (eliminate them)
- In group 5, We will have H21 which can be among top 3 horses.
- H11 was second in Group 6 result.
- In group 3, We can take one horse which can come third.
- We can eliminate the slowest horse from group 3 i.e. H13.
- In group 3, we can have H11, H12, which can be among top 3 horses.
- H1 was first in Group 6 result.
- In group 1, H2 and H3 can come among top 3 horses.
- Finally we will have, H2, H3, H11, H12, H21 horse which can be among top 3 horses.
- We will arrange 7th race to find second and third fastest horse.
- Suppose result of 7th race is H2, H12, H11, H2, H21
- Top 3 horses among 25 horses in 7 races are H1, H2 and H12.
Answer: We need 7 races to find top 3 horses among 25 horses.