相关论文: Applying constraint programming to minimal lottery…

The rules of Sudoku are often specified using twenty seven \texttt{all\_different} constraints, referred to as the {\em big} \mrules. Using graphical proofs and exploratory logic programming, the following main and new result is obtained:…

Given $n$ colored balls, we want to detect if more than $\lfloor n/2\rfloor$ of them have the same color, and if so find one ball with such majority color. We are only allowed to choose two balls and compare their colors, and the goal is to…

Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…

We revisit the classic 'guess my number' game and extend it from its familiar binary form to representations in any integer base. For each base we derive formulas for the number of cards needed to identify a given integer and, conversely,…

This article introduces recursive relations allowing the calculation of the number of partitions with constraints on the minimum and/or on the maximum fragment size.

At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…

The lottery ticket hypothesis has sparked the rapid development of pruning algorithms that aim to reduce the computational costs associated with deep learning during training and model deployment. Currently, such algorithms are primarily…

The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a…

The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player…

We investigate the decomposition problem of balls into finitely many congruent pieces in dimension $d=2k$. In addition, we prove that the $d$ dimensional unit ball $B_d$ can be divided into finitely many congruent pieces if $d=4$ or $d\ge…

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…

It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…

The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…

We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports.

A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…

We prove an interesting fact about Lottery: the winning 6 numbers (out of 49) in the game of the Lottery contain two consecutive numbers with a surprisingly high probability (almost 50%).

This paper studies two families of constraints for two-dimensional and multidimensional arrays. The first family requires that a multidimensional array will not contain a cube of zeros of some fixed size and the second constraint imposes…

The problem of discovering frequent itemsets including rare ones has received a great deal of attention. The mining process needs to be flexible enough to extract frequent and rare regularities at once. On the other hand, it has recently…

Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class;…