It's a bit embarassing how long it's taken me to get through this little book of 53 geometric puzzles. Described as "Bite size problems and multiple ways to solve them", that's exactly what it is. A gift to me from a good friend during the early days of tough times, I think it's taken me more than 18 months to get through them!
They're neat little puzzles, of varying difficulty, but mostly of the kind that you can probably do in your head on a good day, moving up to a few minutes with pen and paper at the end. And this was my downfall! After a decent start, I mostly did try to do them in my head, and not necessarily on good days, and got stuck. Promising myself I'll have a pen and paper next time I look at it, my progress has been very slow but rather enjoyable. Having finally made the effort to have the book and pen and paper at the same time, I've managed to polish the book off.
There are 5 chapters: "What fraction is shaded?", "What's the angle?", "Prove it!", "What's the area?" and "Sangaku problems", each with a different focus. There is a bit of difficulty graduation to it, so there are some you can just pleasantly eyeball, and others where you need to work at it a bit. The puzzles are nicely varied, asking you to work out quite different things; this is not a repetitive book.
The business with "Multiple ways to to solve them" hints at the fact that most puzzles can either be brute-forced or a neat shortcut can be found. The shortcuts are mostly pleasing. There are a few puzzles where I found myself at a loss for an elegant solution, bashed my way through and... yeah, I don't think their answer was elegant either, to be honest! Not all cute puzzles have cute solutions. On the whole, though, my backstop of plugging things into equations and solving for Cartesian coordinates was not necessary. Symmetries get you a long way.
The book itself is published by Tarquin, in that funny space of semi-amateur maths books. The production quality for such books can be... variable, so it's very pleasant for it to be so neat and well-produced. It's very fun, and reminds me of what I'm so happy the whole space exists.
Posted 2023-05-24.