First there was Martin Gardener, then there was Doug Hofstadter, then there was...this Dewdney dude. They were successive writers of the "recreational" column in Scientific American. Dewdney's was "Computer Recreations" and here they are, neatly collected up in a book and updated, too! Except the column ran from 1984-86 and my brother helpful scrawled "1988" in his copy - so it's hideously out-of-date now. There isn't a topic in here that hasn't advanced enormously in the intervening time, perhaps most alarmingly in the discussion of malware, which provoked some readers to write their own disc or network propagated viruses!
That said, because these are recreations, the book has in an important sense not gone out of date; one can still have a go at implementing the simple and not so simple programs discussed oneself - which is the point of these columns, after all - just don't expect to be contributing to the cutting edge of any of these topics anymore.
Some topics were more interesting than others but I think individual opinions on which are most engaging will vary a lot. It's a diverse collection ranging from chaos theory and fractals to mathematical automata (which are a lot more fun than they sound) to simulated zombies and banks to anagrams and pangrams to the aforementioned malware and simple genetic algorithms (which interested me a lot).
The coding challenges seem to become greater as the book progresses but one need not try any of them in order to derive some amusement from this collection - one can live vicariously through the author's discussion of the efforts of the readers of the original articles and see how they got on.