0
votes
0answers
22 views

Diameter of graph formed by pairwise intersections of random chords in a circle

Given n random chords in the circle (a random chord is chosen by specifying both endpoints uniformly randomly from the circumference), form a graph G on n nodes such that an edge exists between i and ...
2
votes
0answers
53 views

Random pair generation?

Suppose there are 6000 people, there will be a combination of $$\binom{6000}{2}$$ ways for 2 people to be chosen out. Now the task is to randomly choose 5000 pairs of people in the total 6000 ...
1
vote
0answers
89 views

Randomized packing of items

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
1
vote
1answer
31 views

linear dependncy of a random vector with respect to a reduced row echelon form in a finite field

Given a matrix with elements from a finite field $\mathbb{F}_q$, $A\in\mathbb{F}_q^{N\times M}$, where $q$ is the size of the field, $N<M$. Suppose that $A$ in the reduced row echelon form. ...
2
votes
3answers
392 views

Random number generator with discrete probability distribution

Is there a general algorithm for implementing a PRNG with a probability distribution?
1
vote
1answer
110 views

Yahtzee Bar Game

A bar near where I work has a game where you pay $5$ dollars which gets you two chances of rolling $5$ dice and if roll results in all of the dice having the same number you win the running pot, ...
0
votes
3answers
81 views

Minimum N to get at least 10 different items in the second draw

I have to randomly choose 50 items out of N possible items. Is there any way to compute N so that, the second time I do this process there is a large probability ( let's say p=0.5) that at least 10 ...
2
votes
2answers
135 views

Probability of a Specific Run Occurring in a Random Process

A random process has three possible outcomes: $A$, $B$, and $C$. At each step, the outcome is decided randomly, and is uncorrelated with previous outcomes. The outcomes occur with probabilities $p_A$, ...
7
votes
2answers
443 views

Probability that a sequence repeats itself

Given an infinite sequence $a_n$ of uniformly random integers $0$ to $9$, what is the probability there exist an integer $m$ such that the sequence $a_1$ to $a_m$ is equal to that from $a_{m+1}$ to ...
4
votes
3answers
202 views

How to generate equiprobable numbers with a random generator?

Is it possible to emulate a 2 sided coin flip (50/50) with a random number generator which outputs equiprobably the numbers 1, 2 and 3 ? If yes, how ? If not why ? Is there a theorem? Can it be ...
10
votes
3answers
2k views

Is there a “most random” state in Rubik's cube?

Is there a state in Rubik's cube which can be considered to have the highest degree of randomness (maximum entropy?) asssuming that the solved Rubik's cube has the lowest?
1
vote
0answers
50 views

An optimization involving (random) graphs

Suppose we have a graph on $n$ nodes. We would like to assign to each node either a $+1$ or a $-1$. Call this a configuration $\sigma \in \{+1,-1\}^n$. The number of $+1$s that we have to assign is ...
2
votes
1answer
166 views

What are the relationships between combinatorics and randomness?

I was just reading the impressive paper by Tim Gowers The Two Cultures of Mathematics when I noticed the various connections between combinatorics and randomness. As a non-mathematician, it is not ...
1
vote
1answer
101 views

pseudo-random permutation of $[0,N)$

Given a positive integer: $$\begin{align*} N \in \mathbb{Z}^+ \end{align*}$$ I would like a function: $$\begin{align*} f : \mathbb{Z}^2 \rightarrow \mathbb{Z} \end{align*}$$ such that ...
2
votes
2answers
63 views

Expectation of random callers distribution

In a country with $N$ people, if everyone calls one random person in the country, what is the expected number of people who dont receive a call? If $f(m,n,a,b)=$Expected fraction of people who ...
4
votes
3answers
370 views

What's the chance of an explicit series of integers in a limited random distribution?

Say I collect 40 perfectly random integers between 1 and 400. What's the chance that any integer is repeated consecutively six times in such a random draw? What I'm looking for is the chance of ...