secrets-of-mental-math-malestrom

Presto-digit-ation: The Art of Mathematical Magic 209
umn, and group of four contains exactly one of these numbers,
each group of four would now add to 34 48 3 85 in the
following magic square.
20 23 29 13
28 14 19 24
15 31 21 18
22 17 16 30
85
As an interesting piece of mathemagical trivia, let me point
out another astonishing property of the famous 3-by-3 magic
square below.
4 9 2
3 5 7
8 1 6
15
Not only do the rows, columns, and diagonals add up to 15,
but if you treat the rows of the magic square as three-digit
numbers, you can verify on your calculator that 492 2 357 2
816 2 294 2 753 2 618 2 . Also, 438 2 951 2 276 2 834 2
159 2 672 2 . If you are curious about why this property happens,
you might want to explore my paper Magic “Squares”
Indeed! (included in the bibliography).
QUICK CUBE ROOTS
Ask someone to select a two-digit number and keep it secret.
Then have him cube the number; that is, multiply it by itself
twice (using a calculator). For instance, if the secret number is
68, have the volunteer compute 68 68 68 314,432. Then