Mathematical Puzzles and Pastimes (Bakst)
Another old math book which was fun to read and which didn't give me a headache in the final chapters (although I might've done more skimming out of disinterest).
While the topics are universal, some of the references are out-dated, such as talk of these new computers and what they will be capable of doing.
Also a little old is the first chapter on "match stick" problems. Many people do these puzzles with toothpicks as they are easier to find these days that wooden matches. (We used to have some around the house as a kid because we needed them sometimes to light the stove -- but we weren't supposed to play with them. Not because we might live them and burn ourselves, but because they didn't want them lost, broken, or scattered underfoot! Plus, people smoked.)
Many of these stick problems were familiar from puzzle books of my youth, or maybe even Boys Life, but I can't say for sure. Some of the others were easy, once you know the basics of moving sticks to make bigger, smaller, or overlapping squares. (Plus, there are a few "trick" questions to get you to think outside the box.) After that, it's a bit repetitive: e.g., move six sticks to make five squares; use the same image and move six sticks to make seven squares. Some of these puzzles you may have accidentally solved during trial and error for earlier problems. And by the end of the chapter, it seems less like brain teasers and more like busywork.
The second chapter was the interesting one. It starts with Billiards geometry (bank shot) and segues into Container Problems. Then using principles for the former, it devises an algorithm for solving the latter, or showing that the problem is unsolvable. (Container problems are the ones were you have, for example, a 12-gallon, 9-gallon, and 5-gallon bucket and you need 7 gallons of water.)
After that, it's a couple of chapters about counting systems, which are basically about using other numbers as bases. The unusual one was bi-quinary, which refers to a counting system that uses two sets of five, instead of ten. Why would anyone do this? Well, the Romans did. If you disallow the use of IV for 4 and instead use IIII (and XXXX, etc), you have a bi-quinary system. 5 I = V, 2 V = X, 5 X = L, 2 L = C, etc.
The other "fun" chapter was the "GOESINTOS", which was about divisibility, and showing it mathematically, without getting so bogged down that my eyes spun. (The notation was not standard, and for this I was grateful. Too many subscripts and superscripts combined give me a headache.) The interesting thing here was the explanation why the Divisibility by 9 rule actually works -- why should adding all the numbers and getting a multiple of 9 prove that the number is a multiple of 9? And why doesn't it work for other numbers? (Actually, it does -- in other bases.)
I could go on, but no one wants that. And if they do, they can look for book reviews on my math blog. mrburkemath.blogspot.com.
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