Related papers: Some Results on the Counterfeit Coins Problem

Faced with a sequence of N binary events, such as coin flips (or Ising spins), it is natural to ask whether these events reflect some underlying dynamic signals or are just random. Plausible models for the dynamics of hidden biases lead to…

In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.

Today, money laundering poses a serious threat not only to financial institutions but also to the nation. This criminal activity is becoming more and more sophisticated and seems to have moved from the clichy of drug trafficking to…

This paper discusses the distributions of missing sums and differences.

The change-making problem asks: given a positive integer $v$ and a collection $C$ of integer coin values $c_1=1<c_2< c_3< \cdots< c_n$, what is the minimum number of coins needed to represent $v$ with coin values from $C$? For some coin…

We discuss a non-intuitive situation concerning percentages.

This paper considers the two-dataset problem, where data are collected from two potentially different populations sharing common aspects. This problem arises when data are collected by two different types of researchers or from two…

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

The counterfeit goods trade represents nowadays more than 3.3% of the whole world trade and thus it's a problem that needs now more than ever a lot of attention and a reliable solution that would reduce the negative impact it has over the…

We discuss some "folklore" results on categorical crepant resolutions for varieties with quotient singularities.

Counterfactuals in quantitative trade and spatial models are functions of the current state of the world and the model parameters. Common practice treats the current state of the world as perfectly observed, but there is good reason to…

Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit in order to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of…

We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

We show that the protocol recently proposed by Hosten et al. does not allow all possible results of a computation to be obtained counterfactually, as was claimed. It only gives a counterfactual outcome for one of the computer outputs.…

One of the earliest cryptographic applications of quantum information was to create quantum digital cash that could not be counterfeited. In this paper, we describe a new type of quantum money: quantum coins, where all coins of the same…

Many studies have shown that there are good reasons to claim very low predictability of currency nevertheless, the deviations from true randomness exist which have potential predictive and prognostic power [J.James, Quantitative finance 3…

In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.