相关论文: The 21 Card Trick and its Generalization

During last years poker has gained a lot of prestige in several countries and, beyond to be one of the most famous card games, it represents a modern challenge for scientists belonging to different communities, spanning from artificial…

Chessboard and chess piece recognition is a computer vision problem that has not yet been efficiently solved. However, its solution is crucial for many experienced players who wish to compete against AI bots, but also prefer to make…

Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know…

We study the Gilbert-Shannon-Reeds model for riffle shuffles and ask 'How many times must a deck of cards be shuffled for the deck to be in close to random order?'. In 1992, Bayer and Diaconis gave a solution which gives exact and…

In the game of pegging, each vertex of a graph is considered a hole into which a peg can be placed. A pegging move is performed by jumping one peg over another peg, and then removing the peg that has been jumped over from the graph. We…

Cops and robbers is a pursuit-evasion game played on graphs. We completely classify the cop numbers for $n \times n$ knight graphs and queen graphs. This completes the classification of the cop numbers for all $n \times n$ classical chess…

Card payment fraud is a serious problem, and a roadblock for an optimally functioning digital economy, with cards (Debits and Credit) being the most popular digital payment method across the globe. Despite the occurrence of fraud could be…

The act of bluffing confounds game designers to this day. The very nature of bluffing is even open for debate, adding further complication to the process of creating intelligent virtual players that can bluff, and hence play, realistically.…

Our ignorance of the winnability percentage of the solitaire card game `Klondike' has been described as ``one of the embarrassments of applied mathematics''. Klondike, the game in the Windows Solitaire program, is just one of many…

Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not…

We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats…

Consider three players Alice, Bob and Cath who hold a, b and c cards, respectively, from a deck of d=a+b+c cards. The cards are all different and players only know their own cards. Suppose Alice and Bob wish to communicate their cards to…

20 Questions (20Q) is a two-player game. One player is the answerer, and the other is a questioner. The answerer chooses an entity from a specified domain and does not reveal this to the other player. The questioner can ask at most 20…

Mahjong is a very popular tile-based game commonly played by four players. Each player begins with a hand of 13 tiles and, in turn, players draw and discard (i.e., change) tiles until they complete a legal hand using a 14th tile. In this…

We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric…

Mirror games were invented by Garg and Schnieder (ITCS 2019). Alice and Bob take turns (with Alice playing first) in declaring numbers from the set {1,2, ...2n}. If a player picks a number that was previously played, that player loses and…

The deduction game may be thought of as a variant on the classical game of cops and robber in which the cops (searchers) aim to capture an invisible robber (evader); each cop is allowed to move at most once, and cops situated on different…

Visual Cryptography is a secret sharing scheme that uses the human visual system to perform computations. This paper presents a recursive hiding scheme for 3 out of 5 secret sharing. The idea used is to hide smaller secrets in the shares of…

We consider the following one-player game called Dundee. We are given a deck consisting of s_i cards of Value i, where i=1,...,v, and an integer m\le s_1+...+s_v. There are m rounds. In each round, the player names a number between 1 and v…

Wordle is a single-player word-based game where the objective is to guess the 5-letter word in a maximum of 6 tries. The game was released to the public in October 2021 and has since gained popularity with people competing against each…