Harry Lorayne's newest book is called, "How to perform feats of Mathematical Wizardry". I've finally managed to get my hands on a copy, so here's the review I promised in my 100th post. First, the basics of the book. It comes as a 202-page, soft-bound book measuring 7.25 by 9.5 inches. Harry Lorayne not only wrote the book, but published it, as well.

Now, what about the contents? The contents are divided into 7 chapters, each with a different theme. Believe it or not, the very first effect the book is the ol' 1089 trick. Wait, come back! This effect is not so much written for its own sake, but as a launching pad for a discussion of the 9 principle, which forms the basis of the majority of the first chapter. If you've ever used the 9 principle in an effect before, but never been quite sure about why exactly it works, the effects and the discussion of them to be of great value. You quickly work up to feats such as adding six 5-digit numbers faster than a calculator, Pascal's triangle (discussed in detail), the classic Fibonacci addition feat (I'm not quite sure why this is in the "9 principle" chapter), and the "Missing Digit" feat. I've always loved this feat, in which someone multiplies two 3-digit numbers together, reads you every digit in the answer except for one of them, and you can name the missing digit (This can be done as a mind-reading feat, a memory feat or a lightning calculation feat)! There's a concept in here that I first learned from Harry's magazine Apocalypse, which is very subtle and clever. I'm almost sad to see it republished.

The second chapter deals with large series and groups of numbers. Here you start by learning how to add consecutive numbers, and then you learn how to take this basic principle into numerous directions . . . literally! There's even an excellent presentational touch for the Fibonacci addition trick that I'd never seen before. This chapter also includes multiplication feats, "Nim" and other object-moving games, and even a brief discussion of those hoary old algebra-based effects. These are the ones that usually begin something like, "Think of any number, add 5 to it, now multiply that by 50..." As is pointed out in the book, anyone with any math sense in your audience will usually see right through these. Even the author mentions that these tricks are included more for the sake of completeness.

Chapter 3 deals with numbers that, due to their special arrangement, give them unique properties that are well suited for mathematical feats. The first half of this chapter concerns feats using the arrangement of numbers on a calendar, including Mel Stover's "Irresistible Force" (which is also discussed in detail on Doug Dyment's website). The latter half of the chapter deals with specific numbers, such as 3,367 and 142,857, which have their own unique features.

Chapter 4 starts with a classic card effect and a classic coin effect (known as "Debit and Credit"), and then quickly moves onto magic squares! If you're thinking that I've examined this chapter more than any of the previous ones, you're right. Basic approaches to 3x3 and 4x4 magic squares are discussed, after which comes the largest single article in the entire book. Harry Lorayne wrote an excellent article on magic squares in the April 2005 issue of Genii, which I reviewed shortly after starting this blog. If you wished you hadn't missed this article, you'll be glad to know that you can find it in full in Mathematical Wizardry. Harry concludes this chapter with the interesting "To-And-Fro Magic Square" (which I'll let you discover for yourself).

Moving on to the fifth chapter, this one deals with rapid division and addition feats. There two major gems in this chapter are the "Additional Adding" routine, in which someone creates a random 6-digit number, and you instantly create a list of four 5-digit numbers that total that number, and the reprint of Alan Jackson's "Diabolical Divisors" from Apocalypse. In the Jackson routine, there are six phases. In each phase, your audience is asked to create random repeating numbers, and you're able to give larger and larger divisors for the numbers each time. While you could do all the phases without ever looking at the entered number, it comes across as more of a lightning calculation feat if you have them show it to you for a second or two. There are some great presentational hints for this effect here, that weren't in the original Apocalypse write-up. This routine is hidden at the end of the plainly-titled "Another 'Combination'" routine, so I haves this will help it remain hidden, and I can keep using it to amaze people.

The sixth chapter is dedicated to classic routines of varying types. The first routine is the recall of the day of the week for any date in the current year, which I've talked about numerous times on this blog. Even if you just do the current year, as opposed to the version in which you can do any year, this is very impressive. Right after that, there's Hummer's classic 3-object divination. Here, you're taught the classic version, as well as a version in which you don't even have to look at the items to determine the mentally chosen object. If you're not familiar with Hummer's 3-object divination, you need to get this book just for this routine. Ever since I first discovered this effect in the March 1990 issue of Genii, I've had it in my arsenal.

Many books of effects have at least one "hodge podge" chapter, a chapter in which everything that didn't fit else into the other sections is presented. This chapter includes some feats that could also be used as memory feats. There's the memory magic square, originally from Lorayne's Reputation Makers. Also along this line is "TAELBPAH", in which you learn to say and/or write the alphabet backwards and forwards, at the same time. This is not only an impressive feat on its own, but would also work well as a closer for those who do "Learning the Almost Impossible", the routine in which you teach the audience to say the alphabet backwards from the first volume of Mentalism Incorporated. Among the puzzles and odds and ends in this chapter, you also learn how to square any two digit number mentally.

One of the criticisms of this book is that so much of the material has seen print before. This is true. For example, you can learn a two-digit squaring method on the Mathpath site. In Harry's favor, he often presents new touches for these older feats that really helps improve their presentation. Also, there are enough routines here that I haven't run across that often, that do make this book valuable. The quality of the material as a whole is also much higher than the average collection of mathematical magic.

Overall, I would recommend this book to those who are looking for a great collection of mathematical routines in a single book.