SOLUTION: If the prize pool is $2000 and I’m in 856th place out of 3,000 people, how much would I receive from the prize pool?

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Question 1209129: If the prize pool is $2000 and I’m in 856th place out of 3,000 people, how much would I receive from the prize pool?
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the prize pool is $2000 and I’m in 856th place out of 3,000 people,
how much would I receive from the prize pool?
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Generally speaking, the rules of the game / (of the competition) should be established by the problem.


But since the problem does not establish the rules, I will establish them myself as I like to establish them. 


Naturally, I will establish the rules by the most simple way, 
throwing aside all the details that are unnecessary to me.


In particular, I will assume that the dollar is divisible by any integer number of parts.


So, let the rule is dictated by this table 

             Last                          First

     Place   3000  2999  2998  2997  . . .   1

     Prize     d    2d    3d    4d   . . . 3000d


where  "d"  is some real number of dollars, not necessary integer number, 
but, perhaps, any rational number of dollars.


Then the unique restriction is for the sum

    S = d + 2d + 3d + . . . + 3000d = 2000  dollars.


It can be written in the form

    %283000%2A%283000%2B1%29%2F2%29%2Ad = 2000,

or

    4501500*d = 2000,  d = 2000%2F4501500 = 20%2F45015 dollars.


Hence, the person on the 856 place will get  %28%283000-855%29%2A20%29%2F45015 = 0.953015661 dollars.


You may treat it in any way you want.

Solved.