Related papers: Some Results on the Counterfeit Coins Problem
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
This paper reviews and summarizes the research results on fact-based fake news from the perspectives of tasks and problems, algorithm strategies, and datasets. First, the paper systematically explains the task definition and core problems…
A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…
ApSimon considered the problem of deciding by a process of two weighings on which of a known number of mints emit either coins of a known genuine weight or emit coins of a different secondary but unknown weight. The combinatorial problem…
In this paper, we devote our interest to solving the real cubic truncated moment problem. We provide some results that allow to get a complete solution via a minimal representing measure. Some numerical examples are also presented to…
In this paper, we give a new bijective proof of a multiset analogue of even-odd permutations identity. This multiset version is equivalent to the original coin arrangements lemma which is a key combinatorial lemma in the Sherman's Proof of…
This paper presents a collection of experimental results regarding permutation pattern avoidance, focusing on cases where there are "many" patterns to be avoided.
Polymer banknotes are the trend for printed currency and have been adopted by more than fifty countries worldwide. However, over the past years, the quantity of polymer counterfeits has been increasing, so has the quality of counterfeits.…
Many proposals for the design and implementation of digital wallets assume that the purpose of the wallet is to enable offline payments via custodial accounts, ignoring the real problems faced by individuals and businesses that engage in…
Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
Counterfeiting of manufactured goods is presented as the theft of intellectual property, patents, copyright etc. accompanied by identity theft. The purpose of the identity theft is to facilitate the intellectual property theft. Without it…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
I introduce, solve and generalize a new coin puzzle that involves parallel weighings.
We give a sketch for an alternative proof of a recent result by J. Tseng.
Fake currency, unauthorized imitation money lacking government approval, constitutes a form of fraud. Particularly in Afghanistan, the prevalence of fake currency poses significant challenges and detrimentally impacts the economy. While…
This talk provides a short overview of recent results on possible CPT violation and some associated experimental signatures.
Manipulated videos, especially those where the identity of an individual has been modified using deep neural networks, are becoming an increasingly relevant threat in the modern day. In this paper, we seek to develop a generalizable,…
The paper reviews rigorous results about quantum dots, in particular exact solutions for few electron dots and limit theorems for high magnetic fields and/or high electron number.
We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…