Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [fair-division]

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

3
votes
1answer
45 views

Fair Sharing of a Pizza When Opinions About the Edge Differ

Two friends wants to share a pizza. One of them loves the edge of the pizza and the other one hates it. Both consider the pizza to get tastier the closer to the center you get. What is the fairest way ...
0
votes
1answer
45 views

Fair choosing rotation with 8 people

I have to divide holiday shifts at work into a group of 8, both AM and PM shifts need to be covered (we rotate between both AM & PM). A total of 24 holiday shifts with 3 major holidays (New Years, ...
0
votes
0answers
19 views

Cake cutting when some players don't like cake

I am beginning to acquaint myself with the fair division literature. So far, I've always encountered the assumption that the value functions $V_i$ are normalized, such that $V_i([0,1])=1$. But it ...
0
votes
2answers
32 views

Game theory problem about 2 students claiming different work amounts

This is quite a simple question I heard and wondered what the mathematical absolute solution to it. There are 2 students, the teacher saw their group project and graded it 100 points. Now he needs ...
0
votes
3answers
36 views

Different Remainders of Three Digit Numbers

I have come across an Olympic Maths style of question. At first glance, the question seemed simple. After going deeper into the question, I couldn't find any shortcut or simple formula to calculate it ...
9
votes
1answer
49 views

Best way to divide multiple equal groups into known unequal groups. 🎄Christmas Lights🎄

I'm not a math guru, but I do like Christmas lights. I am helping set up a decent sized lighting display for my work, I have measured all outlines and props to figure out how many lights we are ...
0
votes
0answers
13 views

Weighted and exponential distribution

I have no advanced mathematics knowledge and I would like to come up with a formula that would express my thinking. I have a pot of money of $1,000 that I would like to distribute to 3 persons ...
0
votes
1answer
26 views

Organizing objects in a near-square pattern

I don't have any fixed constraints but just a general idea. This probably a well known problem too - yet I can't seem to find any literature on it. Given n identical 2D objects, what is an algorithm ...
2
votes
2answers
69 views

Fair cutting of a cake [duplicate]

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 ...
61
votes
3answers
6k views

Optimal strategy for cutting a sausage?

You are a student, assigned to work in the cafeteria today, and it is your duty to divide the available food between all students. The food today is a sausage of 1m length, and you need to cut it into ...
2
votes
1answer
20 views

Problem involving directly and inversely proportional division

A father wishes to divide his 500-acre farm between his three sons in portions of land directly proportional to the number of kids each one has and inversely proportional to their incomes. If the ...
5
votes
2answers
168 views

The Abel-and-Cain Urn Problem

An urn contains three distinguishable kinds of balls, say $A,B,C$. Abel bets to get, in $t$ trials with replacement, at least one ball of kind $A$ and at least one ball of kind $B$. Cain bets to ...
0
votes
1answer
32 views

How to share a cash prize among multiple entries in position A, B and C

How to share a cash prize among entries in position A, B and C. Each position can have multiple entries. Each entry in position A should have 50% more of the cash prize than each entry in position B. ...
1
vote
0answers
23 views

Fair sharing sequence for n players

When $2$ players are given an infinite stream of items to divide between them. There is no way to quantify the value of the items, but their value is strictly decreasing. Which person should take the $...
0
votes
1answer
23 views

If 1x item costs 310, how much of item would 50 get me?

I'm trying to work out what to use to work this out. If ITEM costs 310 for 1, how much would I get if I paid 50? I'm more looking for how to work this out so that I can apply this to other things.
0
votes
0answers
48 views

how to use full amount in division

How to use the full amount in a division? So if I want to divide 10 / 3, I want the following results [ 3.33, 3.33, 3.34 ] (if ...
-1
votes
1answer
51 views

Renting a house!

Suppose that we are $6$ guests for renting a house, $2$ are going to spend three nights in the house while $4$ of them are going to spend just $2$ nights in this house. The problem is that if the bill ...
0
votes
1answer
304 views

Shapley values- airport problem

can anyone help me on this? I am trying to understand how can I find the Shapley values for the following airport problem. There are 3 types of airplanes, type 1, type 2 and type 3 and they require ...
2
votes
2answers
172 views

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 ...
2
votes
2answers
9k views

Find the greatest number of 6 digits exactly divisible by 24,15 and 36

I am solving questions related to number theory. I have encountered this problem in my textbook. I asked for the solution of this question from my friend. The solution was like this, We will find out ...
3
votes
3answers
70 views

cant understand this basic division

My long division of $0.5$ into $2.5$ gives the answer $4.1$ , but $0.5 \times 4.1$ does not equal the dividend of $2.5?$ so what gives here?
0
votes
1answer
25 views

How to divide based on fraction per partipant

I want to fairly divide a random number of sweets I buy every day between kids in my class for the day based on the days test results. I calculate the test results. There are 10 Kids: At the end of ...
0
votes
1answer
30 views

How to split a total into smaller disaggregates that match the total it was split from

I need to resolve the following in computer language. I have situations that I have to split totals in smaller various disaggregations. A client gets data from clinics around a district. However ...
4
votes
2answers
88 views

Why division gives equal parts?

I'm ashamed to ask this question. For a while, I can't pull out of my mind really basic kindergarten questions like: what is actually a number, what is a function and what is the connection between ...
0
votes
2answers
78 views

Division of a negative number by a positive number

If $-17$ is divided by $3$ below which will be the correct result and why? Quotient is $-5$ and remainder $-2$ Quotient is $-6$ and remainder $+1$
5
votes
1answer
219 views

What's the fairest turn sequence for n players?

For two players, in some sense, the fairest possible turn order is the Thue-Morse-sequence: 01101001100101101001011001101001.... It arises by taking turns ...
3
votes
0answers
365 views

Problems with the Bounded Envy-Free Cake Cutting Protocol of Aziz & Mackenzie [2016]

The problem I'm seeing is with Case 2 of Lemma 4.5 in the latest version of the ArXiv preprint: Unallocated contested piece a has proper trims on it (recall that we are ignoring part that is left ...
4
votes
4answers
108 views

Treating $\frac{n}{0}$ as a constant? [duplicate]

Is there any way of treating $\frac{1}{0}$ without breaking maths? I tried just the variable $\lambda$, thinking that it would be easy to manipulate: $$\frac{2}{0} = 2\cdot\frac{1}{0} = 2\lambda$$ But ...
3
votes
1answer
73 views

Envy-free cake division. What else possible?

According to Selfridge and Conway, 3 people’s method is as follows.(See ref for graphical intuition. And refer to wikipedia for more formal description.) Alice cuts [into what she thinks are thirds]. ...
7
votes
2answers
263 views

Equal slicing of my spherical cake

Recently I baked a spherical cake ($3$ cm radius) and invited over a few friends, $6$ of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited ...
2
votes
1answer
58 views

Spherical Cake and the egg slicer

Recently I baked a spherical cake (3cm radius) and invited over a few friends, 6 of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited ...
0
votes
3answers
86 views

One distributes $10$ cookies evenly between $0$ people. How much does each person get?

This "task" is supposed to show the problems with dividing by zero. However, how does one resolve this? There is no correct answer, since there are no people you could make the statement about. Every ...
0
votes
2answers
1k views

How to approximate the division by a number like prime number?

I was solving some mathematical questions and have come across the situation, where I need to divide 3900/139. Here is my question, a. Can I assume 139 to 140 for the ease of division? If so, how ...
1
vote
1answer
32 views

Fairness problem

I need to figure it out how without exceeding the use of the number 10, find three different ways of distributing some blue and red marbles in a container, so that the probability of randomly ...
1
vote
0answers
55 views

Maximal cake-cutting

Alice and George divide a cake between them. The cake is a 1-dimensional interval and both players value the entire cake as 1. The valuations of the players are represented by non-atomic measures on ...
1
vote
1answer
147 views

Is my cake split envy-free (and coalition-resistant)?

I once read that splitting a cake in 4 parts envy-free is notoriouse difficult. Not to mention splitting it with 5 or more people. Methods involve arbitrarily long recursions and cake split onto ...
3
votes
1answer
143 views

Consensus division of a cake

There is a pie and two people with different tastes. The goal is to cut a piece, using two radial cuts like this: such that both people agree that the piece has a value of exactly a fraction $p$ of ...
1
vote
0answers
42 views

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 ...
2
votes
2answers
24 views

How many different sized holes must be drilled?

A 'starry sky' that's installed on the roof is made with light fibers in a way, that the roof is surfaced with tiles that have been drilled with a proper number of fitting holes. The light fibers are ...
0
votes
2answers
680 views

Probability of a dice game: win, lose or draw.

$C$ and $J$ play a game. $C$ always starts. $C$ rolls a fair dice first and wins if he throws an even number. If not, then $J$ rolls the dice. If she rolls an odd number she wins. if neither win it's ...
0
votes
1answer
50 views

fairly Select set elements base on element count

Please consider this scenario: For example we have 4 sets that each one has some elements. Case 1) in each case there are 10 elements and we want to select 4 elements from sets.It's obvious that we ...
3
votes
2answers
556 views

Understanding the concepts of division and fractions

$\require{cancel}$ I'm having some issues regarding division so I will start by asking how this concept was developed throughout the ages: What was the first civilization to introduce the idea of ...
4
votes
1answer
136 views

Cutting a pie with a fork

You baked a pie in the shape of a disc, with some cherries spread unevenly on its top. You want to give each of your two children a piece of cake such that: The pieces are congruent - have the same ...
2
votes
1answer
2k views

Divide a set of $n$ elements into $k$ subsets having equal sum

Is there / Can there be an algorithm with acceptable time complexity that solves the following? Given $n \leq 20$ non-negative numbers, determine whether the $n$ numbers can be divided into $k \leq ...
2
votes
2answers
114 views

The fair meat bazaar: Who has right?

In a local town the girl scouts have been selling tickets, and now it is the time to pick winners. The number of winners is yet to be decided. The names are collected in $3$ books. With respectively $...
1
vote
1answer
48 views

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 ...
1
vote
1answer
26 views

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 ...
1
vote
4answers
173 views

Challenge: “Dividing” a number above 0 and ending up with the same, or a greater number (creative task)

Here's a question/challenge for those of you who know quite a bit about math, or enjoy to be creative with what you do know (just for reference: I'm virtually illiterate when it comes to any math more ...
1
vote
1answer
68 views

How to solve this problem? Distributed Game theory?

I have this problem: We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$; We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$; Every player has some ...
2
votes
2answers
299 views

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 ...