Question 845402: I am looking for a mathematical formula (equation) for the following scenario:
A challenge is played by X number of participants.
Each participant contributes the same number of Y points to the challenge (when they join).
Thus, the total points in the challenge at any given time is: X*Y points.
The points ares distributed according to the following rule (for which I need a formula):
1. The person in 1st place, takes 50% of the points.
2. For the remaining (X-1) participants, the remaining points are distributed in a descending order of value.
e.g. Challenge A has 10 participants and each participant puts in 10,000 points. With total points in the challenge being 100,000 points.
Person in the 1st place gets - 50,000 points
The remaining 9 participants get the remaining 50,000 points distributed in a decreasing order of value
For example (one such scenario):
#2 - 12,000
#3 - 10,000
#4 - 9,000
#5 - 8,000
#6 - 5,000
#7 - 3,000
#8 - 2,000
#9 - 1,000
Can this be modeled mathematically?
Thank you.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! z=x*y
p=z/2
p = ½(2a + d(n-1))n
n=x-1
d=-1
a= second prize
in your example,
x=10
y=10000
z=100000
p=50000,
n=9,
d=-1,
a=5559.56
p = ½(2a + d(n-1))n
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