secrets-of-mental-math-malestrom

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Secrets of Mental Math
1 5
2
≈ 1.6180339887 ...
a number with so many amazingly beautiful and mysterious
properties that it is often called the golden ratio.
MAGIC SQUARES
Are you ready for a challenge of a different sort? Below you will
find what is called a magic square. There has been much written
on magic squares and how to construct them, going back as far
as ancient China. Here we describe a way to present magic
squares in an entertaining fashion. This is a routine I’ve been
doing for years.
I bring out a business card with the following written on the
back:
8 11 14 1
13 2 7 12
3 16 9 6
10 5 4 15
34
I say, “This is called a magic square. In fact, it’s the smallest
magic square you can create, using the numbers one through
sixteen. You’ll notice that every row and every column adds to
the same number—thirty-four. Now I’ve done such an extensive
study on magic squares that I propose to create one for you
right before your very eyes.”
I then ask someone from the audience to give me any number
larger than 34. Let’s suppose she says 67.
I then bring out another business card and draw a blank
4-by-4 grid, and place the number 67 to the right of it. Next I