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All real life mathematics is problem solving. And all those fascinated by puzzles are problem solvers at heart. But thinking mathematically is a skill we have to learn and one which it is easy to forget. Recreational mathematicians and students can practice problem solving in different ways. In this book solving puzzles is practiced in a different way from most books they will have seen before: the idea is to sit with a puzzle or two over a number of days and wait for a moment of inspiration or insight to arrive. That is the true mathematical experience!