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hidden race order


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#1 BMAD

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Posted 28 March 2014 - 03:22 PM

The 400 metre dash sprinting event will be held at a field track with 5 lanes. 25 athletes will be participating in total, of which, obviously, only 5 can be running together at a time. Define the minimum number of dashes required to determine the 3 fastest athlets of all, so that they are awarded the gold, silver and bronze medal. Which athletes will be running in each dash?

We assume that each athlete performs exactly the same in each dash. The results of the event will be determined by the relative classification of the athletes and not by their exact times. We only need to determine the 3 fastest athletes and not to follow the exact procedure which usually is followed at such events. (Obviously we cannot use a stopwatch).


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#2 bonanova

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Posted 28 March 2014 - 06:30 PM

Spoiler for first thoughts


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#3 harey

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Posted 28 March 2014 - 09:40 PM

The fastest 5 runners can be determined in 7 heats.

 

....

 

I'll wait for discussion before posting the 7-heat solution

 

Please post, I think that you cannot get more than 3:

Spoiler for

Edited by harey, 28 March 2014 - 09:41 PM.

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#4 the_count

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Posted 29 March 2014 - 09:09 AM

sounds like the classic 25 horse problem


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#5 bonanova

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Posted 31 March 2014 - 05:57 AM

My memory was faulty. Only the three fastest can be determined in seven heats.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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