kaliprasad said:you have 25 horses and you have to pick fastest 3 out of the 25. In each race
only 5 horses can run at the same time as there are only 5 tracks. what is the
minimum number of races to pick the 3 horses without using a stopwatch.
Albert said:now I am interested in the following question:
what is the minimax number of races to ensure the 3 horses can be chosen without using a stopwatch ?
kaliprasad said:My solution
you make the horses into 5 groups of 5 horses each say A,B,C,D,E . have 5 races. then pick the winner of the 5 races and have a race that is race number 6.
Now pick the 3 winners out of the 5. Say the winner is from group A, the 2nd ranked is from Group B and 3rd one is from group C.
now let the 1st 3 positions in group A be A1,A2,A3. in group B be B1,B2,B3. and in group C be C1,C2, C3.
A1 is the 1st. B3 cannot be in top 3 beacuse A1, B1, B2 are faster.
So B3 is ruled out.
C2 and C3 cannot be in top 3 as A1,B1,C1 are faster. So have a race among A2,A3,B1,B2,C1 and choose the 2 fastest. the ranks shall be 2nd and 3rd.
So we need 7 races.
Albert said:very good, but there is a flaut, if actural speeds of B3,C2,and C3 are faster than the speeds of A2 and A3
but they did not have a chance for the last trophies competition ,this sounds strange !
The answer is to use a method called elimination. First, divide the horses into 5 groups of 5. Then, race each group and take note of the top 3 fastest horses from each race. Next, race the top 3 horses from each group against each other. The top 3 fastest horses from this race will be your final winners.
Yes, this method is based on the principles of elimination and has been scientifically proven to be an effective way to determine the fastest horses without the use of a stopwatch.
If there is a tie between horses in one of the races, you can either have a tiebreaker race between the tied horses or include all tied horses in the next race. However, the latter option may result in a longer process.
Yes, this method can be used for a larger group of horses. The only change would be to divide the horses into smaller groups, such as 10 groups of 10, and follow the same elimination process.
Yes, there are other methods such as using a mathematical formula or using a random number generator. However, the elimination method is considered to be the most reliable and efficient method for choosing the fastest horses without a stopwatch.