Intereting Posts

Distinction between 'adjoint' and 'formal adjoint'
If $\lim\limits_{x \to \infty} f(x)$ is a finite real number and $f''(x)$ is bounded, then $\lim\limits_{x \to \infty} f'(x) = 0$
A question related to Pigeonhole Principle
How to prove that a group is simple only from its class equation
Subgroups of a direct product
Notation for image and preimage
Values of hypergeometric functions
Creating an ellipsoidal 3D surface
Calculate circle's offset given distorted ellipse, when projected onto a sphere
Number of functions from n-element set to {1, 2, …, m}
Are there more rational numbers than integers?
To what divisors $a$ of $n$ can Euler's Theorem multiplied by $a$ be generalized, i.e. when is $a^{\phi(n)+1}\equiv a \pmod n$?
factor $z^7-1$ into linear and quadratic factors and prove that $ \cos(\pi/7) \cdot\cos(2\pi/7) \cdot\cos(3\pi/7)=1/8$
Sum of polynomial
Solve the System of Equations in Real $x$,$y$ and $z$

So, let’s say you have 5 friends, and went on a trip together and over different occasions, different people paid for different things, with a plan of combining all the bills together at the end and splitting them evenly across all.

What is the best way of achieving this mathematically?

- An Identity Involving Narayana Numbers
- Probability that team $A$ has more points than team $B$
- Finding the probability that red ball is among the $10$ balls
- Same number of partitions of a certain type?
- Looking to understand the rationale for money denomination
- Positive integers less than 1000 without repeated digits

- Fast way to get a position of combination (without repetitions)
- Parity of Binomial Coefficients
- Verifying Touchard's Identity
- Finding the n-th lexicographic permutation of a string
- number of ways you can partition a string into substrings of certain length
- Formula for $\sum_{k=1}^n k\binom nk^2$.
- How to solve permutation group equations?(discrete mathematics,group theory)
- Probability problem
- Number of ways of reaching a point from origin
- Probability/Combinatorics Question

If you add up the total and divide among the number of people you get the amount each person should have paid. If you add up the bills each person has paid and subtract from the amount they should have paid you have the amount each person owes. These amounts should total to 0.

In terms of optimising, I understand that you want to split this up into person-to-person debts rather than person-to-group and group-to-person debts in such a way as to minimise the number of person-to-person debts. This looks rather like a bin-packing problem, so it is probably NP-complete to optimise.

(From a social point of view, the best solution is probably to have one trusted person collect from those who owe to the group and pay to those who are owed).

If you are interested in broader questions about mathematical insights into fairness questions that arise in fair division, cost allocation, apportionment, etc. take a look at this book for a good introduction: Equity in Theory and Practice, H. Peyton Young, Princeton U. Press, 1994.

- Fundamental theorem of Algebra using fundamental groups.
- Fermat's Last Theorem near misses?
- Find the remainder when $1!$+$2!$+$3!$…$49!$ is divided by 7?
- Expectation of Ito integral, part 2, and Fubini theorem
- Entropy of sum of random variables
- For two problems A and B, if A is in P, then A is reducible to B?
- Prove that $\angle FGH = \angle GDJ$
- 3-regular connected planar graph
- Continuous function from a compact space to a Hausdorff space is a closed function
- How to solve $ 13x \equiv 1 ~ (\text{mod} ~ 17) $?
- For $k<n/2$ construct a bijection $f$ from $k$-subsets of $$ to $(n-k)$-subsets s.t. $x\subseteq f(x)$
- Prove $p^2=p$ and $qp=0$
- Any two norms on finite dimensional space are equivalent
- $\sum_{k=1}^n a_k^3 = \left(\sum_{k=1}^n a_k \right)^2$
- Is this a valid proof of $\lim _{n\rightarrow \infty }(1+\frac{z}{n})^n=e^z$?