Sentence Sudoku Puzzles

Four sudoku puzzles using letters instead of numbers and a Latin Square word puzzle

The Fewest Clues Problem

When analyzing the computational complexity of well-known puzzles, most papers consider the algorithmic challenge of solving a given instance of (a generalized form of) the puzzle. We take a different approach by analyzing the computational complexity of designing a "good" puzzle. We assume a puzzle maker designs part of an instance, but before publishing it, wants to ensure that the puzzle has a unique solution. Given a puzzle, we introduce the FCP (fewest clues problem) version of the problem: Given an instance to a puzzle, what is the minimum number of clues we must add in order to make the instance uniquely solvable? We analyze this question for the Nikoli puzzles Sudoku, Shakashaka, and Akari. Solving these puzzles is NP-complete, and we show their FCP versions are Sigma_2^P-complete. Along the way, we show that the FCP versions of 3SAT, 1-in-3SAT, Triangle Partition, Planar 3SAT, and Latin Square are all Sigma_2^P-complete. We show that even problems in P have difficult FCP versions, sometimes even Sigma_2^P-complete, though "closed under cluing" problems are in the (presumably) smaller class NP; for example, FCP 2SAT is NP-complete

Python for education: the exact cover problem

Python implementation of Algorithm X by Knuth is presented. Algorithm X finds all solutions to the exact cover problem. The exemplary results for pentominoes, Latin squares and Sudoku are given.Comment: 13 pages, 4 figures, 3 table

Solving Sudoku with Membrane Computing

Sudoku is a very popular puzzle which consists on placing several numbers in a squared grid according to some simple rules. In this paper we present an efficient family of P systems which solve sudokus of any order verifying a specific property. The solution is searched by using a simple human-style method. If the sudoku cannot be solved by using this strategy, the P system detects this drawback and then the computations stops and returns No. Otherwise, the P system encodes the solution and returns Yes in the last computation step.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

EXTREME OR NATURAL SUDOKU I

(a) Extreme Sudoku puzzles are usually designed for defying our logical reasonings, so we can counter with the Principle of Least Choice (PLC) by selecting the least likely one when facing the multiple choices of our next move. The harder the puzzle, the more often PLC is recommended to be used; (b) This is the first of many volumes of the condensed collection of my previous lecture series 0-5 for promoting the natural Sudoku (Sudoku with 17 givens). Accordingly, I plan to give a series of lectures, each containing 1 puzzle with illustrative solution and 49 practice puzzles with annotated solutions. All (approximately 5000) natural Sudoku puzzles can be downloaded from Gordon Royle list; (c) The minimum of 17 givens is required for a Sudoku puzzle to not having multiple solutions. There are no extra givens that puzzle makers can maneuver to design extremely hard Sudoku. Therefore, we shall not use PLC at all for our insuing lectures; (d) The purpose of my lectures is for you not to waste time in playing Sudoku. In addition to the introduction of efficient methods, we most importantly screen out those puzzles with multiple solutions in the collection of practice sets for you; and (e) The lectures are presented in the power point format, convenient for any interested instructors to use. I sincerely hope some of you could join me for the completion of 100 lectures of the natural Sudoku, which would be a precious asset of the mankind thanks to Leonhard Euler’s Latin Square

Are cocaine-seeking “habits” necessary for the development of addiction-like behavior in rats?

Drug self-administration models of addiction typically require animals to make the same response (e.g., a lever-press or nose-poke) over and over to procure and take drugs. By their design, such procedures often produce behavior controlled by stimulus-response (S-R) habits. This has supported the notion of addiction as a “drug habit”, and has led to considerable advances in our understanding of the neurobiological basis of such behavior. However, for addicts to procure drugs, like cocaine, often requires considerable ingenuity and flexibility in seeking behavior, which, by definition, precludes the development of habits. To better model drug-seeking behavior in addicts we first developed a novel cocaine self-administration procedure (the Puzzle Self-Administration Procedure; PSAP) that required rats to solve a new puzzle every day to gain access to cocaine, which they then self-administered on an Intermittent Access (IntA) schedule. Such daily problem-solving precluded the development of S-R seeking habits. We then asked whether prolonged PSAP/IntA experience would nevertheless produce ‘symptoms of addiction’. It did, including escalation of intake, sensitized motivation for drug, continued drug use in the face of adverse consequences and very robust cue-induced reinstatement of drug-seeking, especially in a subset of ‘addiction-prone’ rats. Furthermore, drug-seeking behavior continued to require dopamine neurotransmission in the core of the nucleus accumbens (but not the dorsolateral striatum). We conclude that the development of S-R seeking habits is not necessary for the development of cocaine addiction-like behavior in rats