Mark’s Bookshelf: Mathematical Recreations by Maurice Kraitchik

Today’s book is Mathematical Recreations by Maurice Kraitchik. As might be evident to long time readers of my blog, I have a lasting interest in what might be called “recreational mathematics”. This is a particularly challenging thing to define, since so much of what we might consider recreational mathematics unveils deep and mysterious things within mathematics. At the Hackers conference I just attended, we paid tribute to the greatest popularizer of recreational mathematics: Martin Gardner. I opined that he was basically invented recreational math, which met (somewhat surprisingly, and I’d still say incorrectly) with some opposition. One of the counterexamples was Maurice Kraitchik.

Many so-called recreational mathematics books are little more than shallowly described algebra problems. Kraitchik’s Mathematical Recreations rises significantly above that. First published in 1942, it includes a wide variety of topics, including gambling, games, magic squares, number theory, geometry, cryptarithmetic, and permutations. You’ll see some things which you’ve seen before, but probably a few gems that haven’t seen wide coverage. For instance, I found this problem to be fairly nice, from page 140.

A man bets 1/m of his fortune on each play of a game whose probability is 1/2. He tries again and again, each time staking 1/m of what he possesses. After 2 n rounds, he has won n times and lost n times. What is his result?

I’ll leave it to the reader to work out the result, but it does point out clearly that proportional betting isn’t the way to fame and fortune, at least, not if the game is fair (the payout is equal to the odds).

The section on calendars is pretty nice too, including a good description of Gauss’ method for computing calendrical dates, and including a nice nomograph that implements a perpetual calendar. Very good.

Worth having on your shelf.