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Questions tagged [fair-division]

For various problems related to dividing a resource among several parties.

Fair division, also known as the cake-cutting problem, the sandwich-splitting problem, and the pizza-dividing problem, is the problem of dividing a resource in such a way that all recipients believe that they have received a fair amount.

Various versions of this problems appear as logical puzzles in recreational mathematics.

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Cutting the Cake Problem

The traditional method for two children to divide a piece of cake fairly between them is "you cut, I choose". What process accomplishes this is intuitively clear. Is there a similar process which works for $3$ children? Suppose that three children…
anonymous
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Weighted division?

Let's say I have 10,000 dollars I want divided among 10 people. With simple division each person gets $1,000. Easy enough. Now suppose each person has a score on a test from 0 to 200. Now I want to divide the money among all the people but…
User
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Protocol to split a common item between 2 people

I have a question related to the "pizza splitting" problem (split the pizza in a fair way), and I am looking for an answer of hopefully the same elegance (first splits, second chooses). Not sure if this is the right Stack Exchange site to ask this,…
vektor
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Bonus scheme calculation

Problem Background: We are a project based company. Employees work on project basis and each project duration can be between 3 days to 30 days. At the end of each project, the employee will get rated from a score of 1 (worst) to 3 (best) across 5…
upchuck1
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Fair cutting of a cake

For the fair cutting of a cake into n pieces for n people, is it sufficient for one person to cut the cake, and for them to get the last pick of piece? If any one piece is bigger than 1/n, another person will take that piece. If any one piece is…
Yashmnash
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How to divide 276 with 15 people?

I have a math question. In our bachelor room our water bill is 276. It is a bill for 31 days. But out of this 15 people, only 12 people used water for 31 days. one went for vacation after 20 days that means he drank only 20 days. another drank only…
Muhamad Sadik
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Allowance distribution problem

When I say allowance, I mean like the kind you earned as a child. Here is the problem I am trying to solve. A parent has $20 they want to give to the child for doing all of their chores. If the child does all of their chores, they get 100% of their…
Nathan Clark
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Weighted division with min and max bound?

Let's say I have 10,000 dollars I want divided among 10 people. With simple division each person gets $1,000. Easy enough. Now suppose each person has a share in a company. I want to divide the money base on their percentage of their shares in…
saeed khoshbakht
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For 2 people, division of good s is equitable, why following statement is true?

As I said, For 2 people, division of goods is equitable, then One of the following is true 1) The division is envy free 2) If they switch their shares, then the division is envy free. I started by assuming that It is envy-free and tried to prove…
Daniel
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Shipping Question.

I need to work out the most effective way of shipping the following amount of boxes in different containers. 889210 boxes 666911 boxes 444606 boxes 222305 boxes The largest container can hold 4004 boxes The medium container can hold 3432 boxes The…
Kristian Williams
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Money division based on attendance percentage.

I am organizing a tour for the musicians in my orchestra, and I want to create a formula that will reduce the cost of this tour for each musician based on their percentage of attendance at rehearsals. I have $n$ musicians (around 30+), each one has…
Mateusz Mgum
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Fair division of a portfolio

I have a real world problem. There are n monetary items (e.g. a list of stocks, bonds, etc.) in my portfolio and there are m people to whom I will distribute my portfolio. Each item have a monetary value, but selling the items and giving equal…
Daniel
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Fair Division: for $n > 2$

I apologize if this is a dumb question. Basically, I'm wondering if the following is equivalent to the last diminisher procedure. If not, I'm curious why this fails. What I have in mind is as follows: The idea is that the person cutting the cake…
Yonas Oberlin
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Division of losses

Partner A borrows 40000 and invests in business. Partner B borrows 15000 and invests in same business. The business didnt go through. Both Parties invested a total of 55 000. One partner invested more than other. He demands from partner B to share…
zizu 112233
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Real life problem: How many finalists can participate per school?

I have to organize a tournament with following numbers: I have a total of 1338 participants from different schools, and we need to distribute the 16 finalist's places as fair as possible. The students are distributed as follwing: School and number…
math2hard
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