In this book I have endeavoured to show how pure puzzles (that is, puzzles which differ from crosswords, word-play riddles and the like, in that they are not limited to one or more specific languages) can be solved by systematic trial, with the maximum possible assistance from reasoning.
This reasoning may often shorten the solving time considerably. Sometimes the reduction is due to the puzzle being put in a simpler form; we may invert it, for example, and solve it backwards.
In many cases the solution of the puzzle is found by breaking it up into simpler puzzles; this is a very important strategy, which plays a significant role in mathematics, too. Much attention has been given not only to puzzles, but also to puzzle games (for two players) and their complete analysis.
This topic is developed by various worked examples, which include the game of noughts and crosses (also known by the name of ticktacktoe).
Only here and there has use been made of algebraic formulae, and even then to a very modest extent. The sections in which this occurs have been marked with an asterisk; they can be omitted.
Some sections in which the puzzles or the arguments are somewhat difficult have also been marked with an asterisk. So the reader should judge for himself whether he wishes to skip these sections or, perhaps, even give them special attention. Many of the puzzles in this book and various of the puzzle games are original.
However, all sorts of well-known puzzles and games have been treated as well, but even these have been elucidated in as original a way as possible.
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