Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three algorithms for solving Sudoku puzzles. Backtracking, simulated annealing, and alternating projections are generic methods for attacking combinatorial optimization p...

This paper is concerned with the difficulty of crossword puzzles. A model is proposed that quantifies the difficulty of a puzzle P with respect to its clues. Given a clue-answer pair (c,a), we model the difficulty of guessing a based on c using the conditional probability P(a | c); easier mappings should enjoy a higher conditional probability. The model is tested by two experiments, each of whi...

We use experiments to test comparative statics predictions of canonical tournament theory. Both the roles of principal and agent are populated by human subjects, allowing us to test predictions for both incentive responses and optimal tournament design. Consistent with theory, we observed an incentive effect from raising the winner’s prize. However, we also observed several empirical puzzles th...

Iteration presents opposing puzzles for a theory of the imagination. The first puzzle, noted by David Lewis, is that when a person pretends to pretend, the iteration is often preserved. Let’s call this the puzzle of ‘preserved iteration’. At the other pole, Gregory Currie has noted that very often when we pretend to pretend, the iteration does collapse. We might call this the puzzle of ‘collaps...

The conceptual world of AI is inhabited by a number of epistemic puzzles whose role is to provide a test harness environment for various methods and algorithms. In our paper we focus on those puzzles in which agents either collaborate or compete with one another in order to adopt their epistemological situations to their environment. Our goal is to devise a formal model for epistemic interactio...