Create a predictive equation

Tila: Closed
Palkinto: $100
Vastaanotetut työt: 11
Voittaja: JacobTheGiraffe

Winner

Kilpailun tehtävänanto

More info available on public comment board as I answer questions

An eccentric multibillionaire has donated ten of his billions to be distributed gradually over a period of a few years as part of a social experiment, but, he has not made it simple for prospective recipients. Anyone is free to ask for a share of the $10 billion, up to once per day, and each time they will receive some small fraction of the money.

The billionaire (who really is a bit crazy) is advertising his give-away only in small ways, so more people learn of it gradually. He is offering a $50 prize to the first person who can come up with a formula to ensure that the giveaway takes as close as possible to 5 years to complete, and that the amount of money he gives each requestor remains as close as possible to a constant value from day to day.

Assume the following:
1) The number of people interested will ultimately be small enough that the money can be made to last that long without needing to distribute quantities less than a cent.
2) The rate of increase in requestors will rise rapidly at first as an increasing number of people spread the word, but will at some point during the timeframe start to slow, as the knowledge of the giveaway begins to saturate the population.

Design one or more recursive equations which the billionaire can run each day to determine how much each requestor will receive. Then, explain it in words in such a way that the average person could understand.

There are obviously many very good solutions to this, and no one perfect solution. Thus, for every 10 reasonable and unique solutions I receive. I will award additional winners. Prize is $100 for first place winner. $50 for each additional winner up to a maximum of 10 winners.

Suositellut taidot

Winner

Ilmoita samanlainen kilpailu

Työnantajan palaute

“Great work. One of the first submissions and also the best. Thanks!”

jonasgryder, United States.

Julkinen selvennystaulu

Kilpailun järjestäjä
- 9 vuotta sitten
If you won a second prize, you also received instructions on how to collect.
- 9 vuotta sitten
Näytä 1 viesti lisää
1. Kilpailun järjestäjä
  - 9 vuotta sitten
  Sorry for the long wait. I had forgotten you were having difficulty with the collection process. The payment is there, waiting for you to accept.
  - 9 vuotta sitten
2. melchial
  - 9 vuotta sitten
  had given up the payment, but I'm glad you remembered unfortunately I was out a few weeks, the prize would appreciate if repost
  - 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
I posted a project here. Just bid $50 on it. I will award it to you, then upload the solution you gave in the contest, and I will release the $50.
- 9 vuotta sitten
1. melchial
  - 9 vuotta sitten
  I did
  - 9 vuotta sitten
melchial
- 9 vuotta sitten
at least one second prize
- 9 vuotta sitten
vampyfree
- 9 vuotta sitten
oh :((
- 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
I awarded first place to Jacob the Giraffe, as the first with a great solution. There were a few good solutions to the problem, and I awarded 4 second prizes. In the case of duplicate answers, I gave credit to the first entrant. I also gave credit to duplicates that had exceptionally good explanations.
Second prizes went to MSO12; Cipher0xp; Master of numbers, and Melchial.
- 9 vuotta sitten
MasterOfNumbers
- 9 vuotta sitten
Yes, it appears as I was afraid that recent entries are starting to copy existing algorithms precisely... hopefully by coincidence.
- 9 vuotta sitten
1. Kilpailun järjestäjä
  - 9 vuotta sitten
  No matter, I know how to sort by date :)
  - 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
I have sufficient entries, and will end the contest tomorrow. If you have an entry you are working on, please complete it ASAP.
Thanks!
- 9 vuotta sitten
1. tellma
  - 9 vuotta sitten
  Hi, I'm finishing my solution. Are you going to close the contest today?
  - 9 vuotta sitten
mariannedelcu
- 9 vuotta sitten
I am owner of www.dancesportshow.com I have made an alghoritm for multiplayer game ranking. I could adapt my alghoritm to your requirements
- 9 vuotta sitten
vampyfree
- 9 vuotta sitten
3 Stars ****
Probably not, but you never know. :)))))
- 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
Notes on my star ratings:
5 Stars *****
You definitely have one at least a second place award, and possibly a first place award.
4 Stars ****
You have a good chance at a second place award, depending on what else comes in.
3 Stars ****
Probably not, but you never know. It depends on what else comes in.
Two stars or below. **
Completely out of the running.

If two people enter identical solutions, the tie goes to whoever entered first. If solutions are very similar, I will take into account the following:
-Who entered first
-Completeness of explanation
-Simplicity of explanation (ease of understanding) Less important than the first two. Some concepts are easier to explain than others.
- 9 vuotta sitten
JacobTheGiraffe
- 9 vuotta sitten
Hello, how do you plan on awarding prizes? I think these 'contests' on this website only allow one winner so if you want to give 10 more you might have to open 10 more contests. Correct me if I am wrong (I have never posted a job or contest)
- 9 vuotta sitten
Katso 4 viestiä lisää
1. JacobTheGiraffe
  - 9 vuotta sitten
  And can I submit more than one solution and win $50 or more?
  - 9 vuotta sitten
2. Kilpailun järjestäjä
  - 9 vuotta sitten
  Yes, multiple solutions are fine. If two from the same person win, then that person gets two prizes.
  - 9 vuotta sitten
anujbatham
- 9 vuotta sitten
pls see #6
- 9 vuotta sitten
anujbatham
- 9 vuotta sitten
PLS SEE #6
- 9 vuotta sitten
kenbonilla
- 9 vuotta sitten
Can a person make a request more than once, or shall we assume the give away is capped at the population?
- 9 vuotta sitten
1. Kilpailun järjestäjä
  - 9 vuotta sitten
  They may make a request once per day. The total requests per day is capped at the population.
  - 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
As time goes on, the market starts to get saturated. You will, for example, never have more than the world's total population.

Since each day, there is a bit more data to analyze, this will allow you to continue to adjust to get even higher accuracy.

It is not possible to have a single correct solution. It is a matter of coming up with a mathematical strategy to make the best possible guesses.

The value of what each request is worth will vary daily, but the idea is to use predictive equations to minimize those variations while ensuring that there will be sufficient money to give everyone at least $.01 on the last day. Assume that all historical data for number of requests, and amount given per request is always available.
- 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
Entries do not need to be a single equation. There can be a series of equations with the results of one becoming input for another, or different equations depending on results of previous calculations. There can be as many equations and conditions as you need, just put some psudocode or instruction around them so the use is clear.

Example:

p=daily increase in number of requests in percent

If 30 day moving average of x > all days moving average of x, path:
Use equation set 1.
else
Use equation set 2.
end if
- 9 vuotta sitten
Kilpailun järjestäjä
- 9 vuotta sitten
The number of coins distributed daily can't be fixed, since the billionaire cannot know in advance how many people will ultimately make requests. There cannot be a fixed, perfect solution, due to the number of unknowns, i.e. how many people?, will they all request daily? how quickly will requests grow as word spreads? When will it level off? etc.

So, for the first 60 days, you may want to set the amount per request at $.01, and just gather data on rate of increase in requests so you have some basis on which to make a first guess.

After a few days, you will have somewhat of a trend. Is the trend geometric or arithmetic? Is it leveling off, or moving up at an increasing pace. You can take this information to get a rough idea of how much to give each day. As the number of days increase, so does your data set, so you can get increasingly accurate.

Each day, there is one more day of historical data you can use.
- 9 vuotta sitten
anujbatham
- 9 vuotta sitten
if the number of people is fixed then it can be made
- 9 vuotta sitten