Samo Pahor (2016) *NP-completeness of mind games and puzzles*. EngD thesis.

## Abstract

The hardest problems in NP are called NP-complete problems; these are problems that we currently do not know how to solve quickly. There is a variety of NP-complete decision problems in different fields, ranging from graph theory to logic and also note that upon finding a solution to one NP-complete problem, we are able to solve any problem that belongs to the NP-complete class of problems. The thesis will focus on NP-complete problems related to solving puzzles and brain-teasers. We will present a summary of a few well known puzzles and show that they are indeed NP-complete. The proof for their NP-completeness will stem from the existence of transformations (or reductions) between them. For each puzzle we will first present the respective decision problem and then transform the solving of an already proven NP-complete decision problem to solving the decision problem pertaining to each puzzle.

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