Is it harder to solve many puzzles than it is to solve just one? This question has different answers, depending on how you define puzzles. For the case of inverting one-way functions it was shown by Yao that solving many independent instances simultaneously is indeed harder than solving a single instance (cf. the transformation from weak to strong one-way functions). The known proofs of that re...

Artificial Intelligence can be thought of as the study of machines that are capable of solving problems that require human level intelligence. It has frequently been concerned with game playing. In this thesis we shall focus on the areas of search and complexity, with respect to single-player games. These types of games are called puzzles. Puzzles have received research attention for some decad...

We analyze the computational complexity of solving the three “temporal rift” puzzles in the recent popular video game Final Fantasy XIII-2. We show that the Tile Trial puzzle is NP-hard and we provide an efficient algorithm for solving the Crystal Bonds puzzle. We also show that slight generalizations of the Crystal Bonds and Hands of Time puzzles are NP-hard.

It has been observed in recent neuroimaging studies that the anterior cingulate cortex (ACC) is involved in the insightful solving of puzzles. Yet, the exact function of the ACC in insight is not clear. In this event-related fMRI study, we compared the neural correlates of the solving of two kinds of puzzles. In Condition A, the subjects solved a list of puzzles that were constructed by differe...

Conception and calculation method of information entropy is customized for Sudoku puzzles and a corresponding algorithm is designed to solve Sudoku puzzles. The definitions of inverse information entropy and information amount for inverse information entropy are also introduced and directly used instead of information entropy in order to simplify the solving procedure. Experimental results show...

This paper investigates real-time bidirectional search (RTBS) algorithms, where two problem solving agents, starting from the initial and goal states, physically move toward each other. To evaluate the RTBS performance, two kinds of algorithms, centralized RTBS and decoupled RTBS, are proposed and are compared to real-time unidirectional search (RTUS). Experiments on mazes and n-puzzles show th...

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...

Computer applications have intriguing potential for enhancing human problem-solving capabilities. They allow us to play with ideas in their nascent stage and to experiment with possible solutions. Spreadsheet calculators and scripting languages are often used as ad-hoc tools to replace tedious pen-and-pencil work in such circumstances. The author of this article has previously used script langu...