Famous Puzzle Research Articles

Efficient Card-Based ZKP for Single Loop Condition and Its Application to Moon-or-Sun

A zero-knowledge proof (ZKP) allows a prover to prove to a verifier that it knows some secret, such as a solution to a difficult puzzle, without revealing any information about it. In recent years, ZKP protocols using only a deck of playing cards for solutions to various pencil puzzles have been proposed. The previous work of Lafourcade et al. deals with a famous puzzle called Slitherlink. Their proposed protocol can verify that a solution forms a single loop without revealing anything about the solution, except this fact. Their protocol guarantees that the solution satisfies the single-loop condition, by interactively constructing a solution starting from a state that holds a simple single loop, and proceeding via steps that preserve the invariant of encoding a single loop, until the proper solution is reached. A drawback of their protocol is that it requires additional verifications to guarantee a single loop. In this study, we propose a more efficient ZKP protocol for such a puzzle with fewer additional verifications. For this, we employ the previous work of Robert et al., which addressed the connectivity property in a puzzle. That is, we verify that a solution is connected but not split, to be a single loop. Applying our proposal, we construct a card-based ZKP protocol for Moon-or-Sun, which has its specific rule of alternating pattern in addition to the single-loop condition.

Deriving the evidence asymmetry in positive polar questions

This paper explores a famous puzzle about English positive polar questions introduced by Buring and Gunlogson 2000: while in many contexts they seem to indicate nothing whatsoever about what the speaker takes for granted or thinks likely, in contexts that provide evidence against the content proposition of the question, they are infelicitous. This pattern, which I term the "evidence asymmetry", has been particularly troubling for standard accounts of polar questions that treat the positive and negative answers on par with each other. However, given that polar questions are felicitous in neutral contexts, it doesn't have an easy solution: polar questions in general don't seem to place constraints on evidence or context. I propose that polar questions have a fairly weak presupposition requiring just the content alternative to be possible (but say nothing about its negation), and (building on Trinh 2014) that this together with Maximize Presupposition-based reasoning about competitor questions (specifically"or not" alternative questions) can derive the evidence asymmetry. This account does not require the covert evidential marker of Trinh 2014, and essentially proposes that the evidence asymmetry follows from norms for English polar questions.

An Intellectualist Dilemma

AbstractLewis Carroll's famous puzzle leads to an explanatory challenge: what must we know to grasp the logical necessity of deductive arguments? This paper argues that intellectualism lacks a philosophically satisfying explanation to that puzzle.

Resolving the Needham Puzzle: Let the Evidence Speak—An Explanation on the Origin of China's Tobacco Industry

In 1954, the famous British historian Joseph Needham put forward a famous puzzle in the preface to his Science and Civilisation in China: before the 15th century, China's civilization was ahead of that of Western countries, both in terms of economics and technology; however, China suffered a disastrous decline in the subsequent era, while its Western counterparts underwent the Industrial Revolution and became the great powers of the world. Thus, Needham asked, why did the scientific revolution, which had taken place in the Western world since the 16th century, not originate in China? This paper has broken new ground both methodologically and substantively concerning the Needham Puzzle. By applying the data found in Chinese historical bibliographies of China as a proxy for the changes in the knowledge stock, this paper proposes the institutional change hypothesis and provides empirical evidence for the dynamic trend of China’s technological development, thereby providing a possible explanation for the Needham Puzzle. And the loss of human capital in science and technology constitutes a necessary condition for the origin of China's tobacco industry. Because the tobacco planting industry is a labour-intensive industry, rather than a technology-intensive industry.

Chisholm’s Paradox Revisited: Puzzles regarding Contrary-to-Duty Obligations and a Dynamic Solution

A contrary-to-duty obligation (CTD obligation) is a type of conditional obligation that tells us what to do when a primary duty is violated. Chisholm’s Paradox is one of the most famous deontic puzzles about CTD obligations. It is widely believed that Chisholm’s Paradox does not arise for ordering semantics, today’s orthodox semantics for modals and conditionals. In this paper, I propose a new puzzle, the CTD Trilemma, to show that ordering semantics still has difficulties in adequately representing natural reasoning with CTD obligations. I argue that to solve the CTD Trilemma a formal account must attend to two different functions played by ought-statements in our normative reasoning and discourse: ought-statements as normative rules and normative judgments. To formally capture this distinction I develop a new dynamic account of ought-statements and normative reasoning inspired by Frank Veltman’s update semantics for default reasoning. Finally, I show how my update semantics for normative reasoning provides a simple and elegant solution to the CTD Trilemma and explains seemingly inconsistent data about inferences using ought-statements in normative reasoning.

Global governance and gross capital flows dynamics

One of the famous puzzles in macroeconomics, the Lucas (Am Econ Rev 80:92–96, 1990) paradox on “why doesn’t capital flow from rich to poor countries”, continues to exist and shapes capital flows in the modern world. This paper provides cross-country evidence on the role of politico-institutional and financial determinants in gross capital flows dynamics over the period 2000–2016. Using panel regressions incorporating country fixed effects, the study argues that institutional quality rather than the effect of diminishing returns of capital is a key explanation for the “Lucas Paradox”. It corroborates previous empirical evidence that government effectiveness, regulatory quality, rule of law, and political stability remain the most important institutional indicators in determining gross capital flows dynamics, highlighting the symmetric effect. In contrast, voice and accountability, and corruption are not significant determinants of gross capital outflows dynamics. The main contribution of the paper comes in identifying the link between the multidimensional nature of financial development and gross capital flows. The empirical results highlight the significance of the differences in gross capital inflows/outflows depending on the country’s level of financial development. The study shows the significance and predominance of financial institutions versus financial markets in the dissemination of gross capital flows.

Two Forms of Realism

There is a famous puzzle in Rorty scholarship: Did or did Rorty not subscribe to a form of realism and truth when he made concessions regarding objectivity to Bjørn Ramberg in 2000? Relatedly, why did Rorty agree with Ramberg but nevertheless insist upon disagreeing with Brandom, though large parts of the research community hold their two respective requests for shifts in Rorty’s stance to be congruous? The present article takes up the discussion and tries, for the first time, to make sense of Rorty’s insistence that there is a difference between Brandom’s notion of “made true by facts” and Ramberg’s notion of “getting things right” by showing that Ramberg’s appropriateness-conditions are fully compatible with Rorty’s revised interpretation of Davidson’s concept of “triangulation,” whereas Brandom’s inferential “made-true-by-facts”-language game is not. The reason why Rorty agrees with Ramberg but not with Brandom, I argue, is that Brandom’s contemporary concept of objectivity, as developed in his contribution to the debate and in his Making It Explicit, works with a scheme-content distinction, whereas Ramberg’s Davidson-based version does not. As many of his critics suppose, Rorty’s concession to Ramberg entails a substantive revision of Rorty’s position, not just a clarification. However, this new position is not in conflict with Rorty’s most important commitment, namely his anti-authoritarianism. The revised account still does not bind him to the forms of realism and truth that his critics favor. The article explains to which forms of realism and truth Rorty’s concessions to Ramberg commit him instead.

Limitation of analogy in the Sleeping Beauty debate: the case of Singer’s argument

Ever since Elga presented his famous puzzle of Sleeping Beauty, philosophers have debated between the Thirder and the Halfer positions. In his recent article, Daniel Singer proposes a new position, according to which Beauty ought to assign [0, 1/2] to (H) the coin’s landing heads. For this argument, he exploits the similarity between Elga’s original puzzle and Bovens’s modified one. According to Singer, Beauty ought to assign the same credence to H (at the relevant moments) in both versions of Sleeping Beauty. Since Beauty ought to assign [0, 1/2] to H in Bovens’s version, she ought to assign [0, 1/2] to H in Elga’s original version, too. Let us call this “the Impreciser view.” In this paper, I will contend that Singer’s argument fails. First, he depends on false assumptions in defending his Impreciser view. Second, Bovens’s version of Sleeping Beauty turns out to be underdescribed in an important aspect. If we try to provide a fuller description for it, either Beauty does not have to assign [0, 1/2] to H or the thus complemented version of Bovens’s puzzle will fail to be analogous with Elga’s original one. In either case, Singer’s discussion does not establish his Impreciser view.

Innovation, life history and social networks in human evolution.

There is a famous puzzle about the first 3 million years of archaeologically visible human technological history. The pace of change, of innovation and its uptake, is extraordinarily slow. In particular, the famous handaxes of the Acheulian technological tradition first appeared about 1.7 Ma, and persisted with little change until about 800 ka, perhaps even longer. In this paper, I will offer an explanation of that stasis based in the life history and network characteristics that we infer (on phylogenetic grounds) to have characterized earlier human species. The core ideas are that (i) especially in earlier periods of hominin evolution, we are likely to find archaeological traces only of widespread and persisting technologies and practices; (ii) the record is not a record of the rate of innovation, but the rate of innovations establishing in a landscape; (iii) innovations are extremely vulnerable to stochastic loss while confined to the communities in which they are made and established; (iv) the export of innovation from the local group is sharply constrained if there is a general pattern of hostility and suspicion between groups, or even if there is just little contact between adults of adjoining groups. That pattern is typical of great apes and likely, therefore, to have characterized at least early hominin social lives. Innovations are unlikely to spread by adult-to-adult interactions across community boundaries. (v) Chimpanzees and bonobos are characterized by male philopatry and subadult female dispersal; that is, therefore, the most likely early hominin pattern. If so, the only innovations at all likely to expand beyond the point of origin are those acquired by subadult females, and ones that can be expressed by those females, at high enough frequency and salience for them to spread, in the bands that the females join. These are very serious filters on the spread of innovation. This article is part of the theme issue 'Life history and learning: how childhood, caregiving and old age shape cognition and culture in humans and other animals'.

Logical and Nomological Obstacles to Foreknowledge of the Future

A famous puzzle called “Grandmother Paradox” is used to argue against the feasibility of traveling backward in time because of the logical and nomological problems such travel involves, and not only because we don’t have the technology to make it reality. The same kind of problems would be encountered in leaping forward in time and then returning to the time of departure. We argue that a similar family of problems also arise in our having foreknowledge of the future without making any time travel. We point to the mysterious consequences of having access to a being, say a machine or a psychic, that can have infallible knowledge of the future and conveys this foreknowledge to human beings truthfully, without any lies or distortions. The cause of these mysterious consequences is the fact that such machines or psychics will raise logical and nomological complications reminiscent of the ones we encounter in time travel scenarios, and that is a strong reason why infallible foretellers cannot exist. We conclude that we can have foreknowledge of the future, in principle, only within certain narrow limits, if at all.

Designators, descriptions, and artifact persistence

Hobbes' (1672/1913) famous puzzle of the Ship of Theseus – in which a wooden ship's parts are replaced plank by plank, and the old planks are subsequently reassembled to create a second ship – has been the source of debate about the criteria that underlie human judgments of individual artifact persistence. This puzzle has led some philosophers to the paradoxical conclusion that an artifact observed at one time is the same persisting individual as two artifacts seen at a later time. We argue that prior discussions of the puzzle have conflated property persistence (judged in conjunction with a description, like “Theseus' ship”) with individual persistence (judged in conjunction with a designator, like “X”). In three studies, we manipulated the linguistic expression (description, designator) used to label the original object in the puzzle. When participants solved the puzzle in conjunction with a description, they gave systematically high ratings to any object (either or both) that could be inferred to match the description. Yet when participants solved the same puzzle in conjunction with a designator, they gave significantly higher ratings to one post-change object (the object made of the reassembled old parts) than to the other post-change object (the object made of replacement parts). The results suggest that individual persistence judgments concerning the puzzle (i.e., those made in conjunction with a designating expression) are not paradoxical but rather are based on the continuity of the object's parts/material.

Betting on the Bulbs: Tulipmania as a Historical Case of Sequestered Capital

Explanations of the timing of booms and busts have heretofore been either non-existent or ad hoc; consideration of sequestered capital promises to improve matters. Sequestered capital is capital that investors place into activities (such as research and/or development) that are unobservable by others. Tulipmania, a famous puzzle, illustrates that the timing of booms and busts can hinge upon sequestered capital. The 1636 sequestration — that is, planting — of tulip bulbs in the Netherlands in mid-November corresponds to the beginning of the boom in promissory note prices; after planting, neither bulb-arbitrage nor observation of bulb-development were possible. Similarly, the timing of the bust corresponds closely to the time that tulip bulbs would have sprouted and become a signal to investors. The case of tulipmania suggests the potential fruitfulness of investigating the role that sequestered capital played in other historical cases of boom-to-bust.

National Happiness and Genetic Distance: A Cautious Exploration

This paper examines a famous puzzle in social science. Why do some nations report such high happiness? Denmark, for instance, regularly tops the league table of rich nations’ well-being; Great Britain and the US enter further down; France and Italy do relatively poorly. Yet the explanation for this ranking one that holds even after adjustment for GDP and socio-economic and cultural variables remains unknown. We explore a new avenue. Using data on 131 countries, we cautiously document a range of evidence consistent with the hypothesis that certain nations may have a genetic advantage in well-being.

Book Review of The Tower of Hanoi: Myths and Maths (Birkhäuser)

As the title of the book suggests, the central topic of “The Tower of Hanoi – Myths and Maths” by Hinz, Klavˇzar, Milutinovi´c, and Petr is the famous puzzle of the same name. The classic Tower of Hanoi puzzle along with a number of its variations and related puzzles are examined in a rigorous mathematical framework.

The Equity Premium Puzzle in Nepal

The study concentrates on one of the most famous puzzles in asset pricing, the equity premium puzzle, which was first identified by Mehra and Prescott (1985). The paper examines the existence and extent of the equity premium puzzle in Nepalese market. The equity premium puzzle refers to the fact that common stocks have offered a very high real risk premium over that of risk-free bills, which leads to unexplainable high risk-aversion of the investors. The study considers the time period of 1995/96 to 2007/08. The result shows that the equity premium exists in Nepal even though the advent of the premium is low compared to other developed countries. This could be a surprising result given the Nepalese context. It was found that the risk aversion of Nepalese investors is greater than 10 (the upeer boundary set by Mehra and Prescott, 1985) which do not fit the conventional financial theories resulting in unexplainable equity premium puzzle. DOI: http://dx.doi.org/10.3126/bj.v3i1.7509 Banking Journal Vol.3(2) 2013 pp.28-42

Peter Abelard on Material Constitution

: Some scholars have suggested that Peter Abelard has a solution to Allan Gibbard’s famous puzzle concerning a lump of clay and the statue that the clay composes. Although Abelard does not explicitly address an analogue of this puzzle, I claim that an Abelardian solution can be constructed based on principles drawn from his discussions of sameness and difference in his later theological writings. In this study, I first summarize the puzzle and several standard solutions to it. I then present and analyze Abelard’s account of sameness and difference, with special emphasis on his description of the ways in which the matter of a statue is both the same as and different from the statue. I then show how we can reconstruct an Abelardian solution to the problem from these remarks. Finally, I consider whether this Abelardian solution is coherent and plausible. In doing so, I show how the Abelardian solution reveals an underlying tension in Abelard’s later ontology.

A restarted estimation of distribution algorithm for solving sudoku puzzles

In this paper, we describe a stochastic algorithm to solve sudoku puzzles. Our method consists in computing probabilities for each symbol of each cell updated at each step of the algorithm using estimation of distributions algorithms (EDA). This update is done using the empirical estimators of these probabilities for a fraction of the best puzzles according to a cost function. We develop also some partial restart techniques in the RESEDA algorithm to obtain a convergence for the most difficult puzzles. Our algorithm is tested numerically on puzzles with various levels of difficulty starting from very easy ones to very hard ones including the famous puzzle AI Escargot. The CPU times vary from few hundreds of a second for the easy ones to about one minute for the most difficult one.

Review of famous puzzles of great mathematicians by Miodrag S. Petkoviç

Review of famous puzzles of great mathematicians by Miodrag S. Petkoviç

The forward-bias puzzle: Still unsolved

Abstract This article argues that Pippenger’s (2011) “Solution to the forward-bias puzzle” must be regarded as an econometric explanation of the famous puzzle, although it does not offer an exhaustive economic answer to it. Some of Pippenger’s (2011) findings are reproduced and established in a cointegrated multiple time series model. It is suggested that economists should stop trying to working out the forward-bias puzzle and start looking for fundamentally better models of foreign exchange rate determination. A tentative alternative is provided.

Famous puzzles of great mathematicians

This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. The selected problems do not require advanced mathematics, making this book accessible to a variety of readers. Mathematical recreations offer a rich playground for both amateur and professional mathematicians. Believing that creative stimuli and aesthetic considerations are closely related, great mathematicians from ancient times to the present have always taken an interest in puzzles and diversions. The goal of this book is to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework. Concise biographies of many mathematicians mentioned in the text are also included. The majority of the mathematical problems presented in this book originated in number theory, graph theory, optimization, and probability. Others are based on combinatorial and chess problems, while still others are geometrical and arithmetical puzzles. This book is intended to be both entertaining as well as an introduction to various intriguing mathematical topics and ideas. Certainly, many stories and famous puzzles can be very useful to prepare classroom lectures, to inspire and amuse students, and to instill affection for mathematics.