Related papers: A note on the counterfeit coins problem
In this paper, we will give an improvement on the lower bound for the counterfeit coins problem in the case that the number of false coins is unknown in advance
In this paper, we will present some results on the counterfeit coins problem in the case of multi-sets.
We address a well-known problem in combinatorics involving the identification of counterfeit coins with a systematic approach. The methodology can be applied to cases where the total number of coins is exceedingly large such that brute…
This work deals with a classic problem: "Given a set of coins among which there is a counterfeit coin of a different weight, find this counterfeit coin using ordinary balance scales, with the minimum number of weighings possible, and…
The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ``balanced'' or ``tilted'' information and that we know the number k of false…
In this expository paper we discuss a relatively new counterfeit coin problem with an unusual goal: maintaining the privacy of, rather than revealing, counterfeit coins in a set of both fake and real coins. We introduce two classes of…
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists,…
In 2007, a new variety of the well-known problem of identifying a counterfeit coin using a balance scale was introduced in the sixth International Kolmogorov Math Tournament. This paper offers a comprehensive overview of this new problem by…
Suppose we are given a set of t coins which look identical, but a known number s of them are counterfeit, with a known weight different from the others. Our problem is to locate the counterfeits by weighing subsets of the t coins, with as…
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns weighing coins on a two-pan scale, under the condition that…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the…
Fake coin problems using balance scales to identify one fake coin and its type among n coins (n > 2) were solved by Dyson in 1946. Dyson gave adaptive solutions with the minimum number of weighings where later weighings may be dependent on…
ApSimon's Mints problem is a very difficult and often misunderstood counterfeit-coin puzzle. I explain the problem and suggest ways to approach it, while giving several fun exercises for the reader.
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…
We discuss coin-weighing problems with a new type of coin: a chameleon. A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently. We consider a mix of $N$ coins that include…
In this paper, we will continue to estmate g_1(n|m) for general n and m.
In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We…
We investigate the structure of the currencies (systems of coins) for which the greedy change-making algorithm always finds an optimal solution (that is, a one with minimum number of coins). We present a series of necessary conditions that…
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…