Please help me with the following question of calculation

[hydraflap]

There are 25 bicyclists and just 5 bicycles. Of all these we need to
find best 3 cyclists. How many races should be held to determine top
three winners and why?

 

 

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Edited February 25, 2013 by imatfaal
Mod Edit Removed link advertising other site.

[imatfaal]

11 races easily does it - but I am sure it can be much quicker.

 

1. choose 5 people - race keep fastest three

2. use fastest three from race 1 add 2 more that have not yet competed - race keep fastest three.

3. rinse and repeat for 9 more iterations - fastest 3 are fastest of whole lot

9 is possible

 

1. race everyone in 5 races of 5 - no one races twice

6. race the 5 best placed in the 5 first races against each other

7. race the 5 second places against each other

8. race the 5 third places against each other

9. race 2nd and 3rd in race 6, against 1st and 2nd in race 7, and first in race 8

 

order is:

winner of race 6

winder of race 9

second of race 9

[Bignose]

this is a truly open-ended question, in that given the information above, there is no right or wrong answer.

 

for example, should we assume all 5 bicycles are identical?

 

then, there are many different ways to determine the 'best' 3.

 

You can have 5 cyclists each do a heat compromising 5 heats. Take the winner from each heat in one race, and determine 1st, 2nd, and 3rd from that.

 

Or, you can run several heats and simply take the best aggregate times and declare them 1st, 2nd, 3rd.

 

Or, using those aggregate times set up a seeded 1-on-1 tournament, with the losers of the semifinals matches racing to determine 3rd.

 

Or, you could just do a randomized tournament.

 

etc. etc.

 

All of these methods have various advantages and disadvantages. You'll find all of them and many more methods used in various sports today. Often depending on what the governing body of each sports thinks are the most important advantages of each method, including but not limited to entertainment value.