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Algebra/Olympics Games Medals.

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Question
Dear Prof Scott

http://en.wikipedia.org/wiki/Olympic_Games
http://en.wikipedia.org/wiki/Olympic_medal
http://en.wikipedia.org/wiki/Metal

We see that there are three medals given to the Top Three Winners of the Indoor/Outdoor Games. i.e Gold, Silver and Bronze.

Queries
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Why only Top Three ?. why not Top Four or Top Two winners considered by the Olympic Committee ?.

Suppose Four medals are given that means there are Top four winners. So in this case What will be the Medals ?

Gold, Silver, Bronze, Aluminum ?

Suppose Two medals are given that means there are Top Two winners. So in this case What will be the Medals ?

Gold, Silver ?.

So why the Number 3 and not 2,4, Any number > 3 were/are considered.

Thanks & Regards,
Prashant S Akerkar

Answer
Why only the Top Three?  Why aren't the Top Four or the Top Two winners
considered by the Olympic Committee?

 The top three in each event are considered since that's what's done in almost any other race
 and has been done for such a long time.

Suppose Four medals are given that means there are Top four winners.
So in this case, what will be the Medals?  Gold, Silver, Bronze, Aluminum ?

 Almost any medal could be considered that is more common than bronze,
 and aluminum sounds like a good choice.

Suppose Two medals are given that means there are Top Two winners.
So in this case, what will be the Medals?  Gold, Silver?

 That would be a good choice, for those are the two most expensive medals.

 They could just as well be bronze and copper, but that wouldn't seem very good to the winners.


So why the Number 3 and not another number?

 If they wanted to, they could considere any number.

 If they didn't consider giving anyone a medal, what would be the point of going
 to compete?

 If they only gave out a medal to 1st place, people would wonder who got 2nd or 3rd.

 They give out medals to the 1st three positions so that the people who got 1st, 2nd, and 3rd
 get some reward for doing that.

 If they really wanted to, they could give out as many medals as they wanted to.
 For example, maybe they wanted to give out 5, and then they could make them
 gold, silver, bronze, aluminum, and steel.  In most cases, however, only the top three
 positions in a race or other sporting event are looked at.

 If they felt like doing something radically different, they could give out 10 medals in each
 event, each medal a lower quality of gold than the last one.  This started way back in the
 Greeks, however, and they most likely awarded the first three in each event as well.

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