Related papers: \AE quitas: Two-Player Counterfeit Coin Games
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…
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…
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…
As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can change its weight. The coin can pretend to be a real coin, a…
In this paper, we will present an algorithm to resolve 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.
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…
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,…
Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…
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…
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…
There are many papers written on the Two Envelopes Problem that usually study some of its variations. In this paper we will study and compare the most significant variations of the problem. We will see the correct decisions for each player…
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
We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial…
The Chinos game is a non-cooperative game between players who try to guess the total sum of coins drawn collectively. Semiclassical and quantum versions of this game were proposed by F. Guinea and M. A. Martin-Delgado, in J. Phys. A: Math.…
We devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has…
We provide a mechanism that uses two biased coins and implements any distribution on a finite set of elements, in such a way that even if the outcomes of one of the coins is determined by an adversary, the final distribution remains…
We present a two-party protocol for quantum gambling, a new task closely related to coin tossing. The protocol allows two remote parties to play a gambling game, such that in a certain limit it becomes a fair game. No unconditionally secure…
We study games in which every action requires planning and preparation. Moreover, before players act, they can revise their plans based on partially revealing information that they receive on their adversary's preparations. In turn, we…
Two players alternate tossing a biased coin where the probability of getting heads is p. The current player is awarded alpha points for tails and alpha+beta for heads. The first player reaching n points wins. For a completely unfair coin…