Divide x into y parts by decreasing amount

Question

If I had $1000(variable) and I want to split that amount up and give it to 20(variable) people, but rather than give it evenly to each person, I want to give more to the 1st per

Answer 1

Adding answer to Ensure prize pool doesn't award tied participants less than participants who scored worse

Two things

1. Incorrect, when assigning prices start from first person to the n-1 one person does't get prize, correct is start from first person to the n

2. Valid basePrize noted with K is

   k = (2 * prize) / ((people) * (people + 1))

Now the answer the other question:

int totalPeople = 20;
float prize = 5000;

List peopleScores = new List();
Random r = new Random();
for (int i = 0; i < totalPeople; ++i)
{
    peopleScores.Add(r.Next(0, 100));
}

var totalPeopleWithScore = peopleScores.Where(x => x > 0).Count();

var groupedScores = peopleScores
    .Where(x => x > 0)
    .ToList()
    .GroupBy(x => x)
    .Select(grp => new
    {
        score = grp.Key,
        peopleScores = grp.ToList()
    })
    .OrderBy(g => g.score)
    .ToList();

var groupCount = groupedScores.Select(x => new { count = x.peopleScores.Count() }).Select(z => z.count).Count();

float basePrizeRate = 2 * prize / totalPeopleWithScore / (totalPeopleWithScore + 1);
Console.WriteLine("Base Price rate: " + basePrizeRate);
float sum = 0;
var leaderboardPosition = 0;
var totalWinners = 0;
foreach (var positionScore in groupedScores)
{
    var countWinner = positionScore.peopleScores.Count();
    Console.WriteLine();
    Console.WriteLine($"On leaderboard position : {groupedScores.Count() - leaderboardPosition} are {countWinner} winners with score: {positionScore.score}");

    float positionPrizePool = 0;
    for (int i = 1; i <= positionScore.peopleScores.Count(); ++i)
    {
        totalWinners++;
        positionPrizePool += totalWinners * basePrizeRate;
    }
    Console.WriteLine("Prize Pool " + positionPrizePool);
    var personPoolPrize = positionPrizePool / positionScore.peopleScores.Count();
    foreach (var x in positionScore.peopleScores)
    {
        Console.WriteLine($"Winner {totalWinners} won: {personPoolPrize}");
        sum += personPoolPrize;
    }
    leaderboardPosition++;
}
Console.WriteLine();

Console.WriteLine("Total Prize: " + sum);
Console.WriteLine("Total Winners: " + totalPeopleWithScore);