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# Horse Puzzle

## Horse Puzzle

There are 25 horses among which you need to find out the fastest 3 horses. You can conduct race among at most 5 to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out how many races are required to get the top 3 horses.

Solution:

Step 1:

• Distribute all the 25 horses in such a way that there  is 5 horses in each group.
• Now, we conduct a race among these 5 groups in the race course

Step 2:

• From the image we can conclude that each row represents the race of 5 horses each.
• For easier approach we will name each horse based on his position in his respective row and column.
• Therefore, the first Race(row 1), was contested between the horses A1B1, A1B2, A1B3, A1B4, and A1B5 .
• The second race was contested between A2B1, A2B2, and so on. and similarly till fifth race.
• Now by the image we can say that the fifth horse from each row won the race i.e., A1B5, won the first race

Step 3:

Now after placing each horse in its position we can conclude that the fifth horse from each row won the race i.e.,

• Winner of first race: A1B5
• Winner of second race: A2B5
• Winner of third race: A3B5
• Winner of fourth race: A4B5
• Winner of fifth race: A5B5

Similarly for second position,

• Second place in first race: A1B4
• Second place in second race: A2B4
• and so on

The same will follow for third position i.e., the third member of each group came third:

• Third position in first race: A1B3
• Third position in second race: A2B3
• and so on

Step 4:

Now we will conduct a race among the winner of each race i.e., among A1B5, A2B5, A3B5, A4B5, and A5B5

Lets say A1B5 wins this race, A2B5 comes second, and A3B5 comes third.

Step 5:

• Now, the winner of this race (A1B5) is the fastest horse of the among all others in the group.
• Now, the horse which is second in the entire group can either be A2B5 or A1B4.
• The horse which is third in the entire group can either be A3B5, A2B4 or A1B3.
• Therefore, we race these 5 horses.

Step 6:

Therefore, the horse A1B5 is the fastest horse. The horses which come second and third in the last race are the horses which are second and third in the entire group respectively.

Conclusion:

In this way, the minimum number of races required to determine the first, second and third horses in the entire group is 7.