(a) If English is your mother tongue, try work
ing on word puzzles. Many daily newspapers
carry the Jumble puzzle, in which you unscram
ble anagrams (permutations of the letters of a
word). For example, djauts is adjust. Try to
get to the point where the anagrams unscram
ble themselves unconsciously, almost instanta
neously. This taps into your mind's amazing
ability to make complicated associations. You
may also find that it helps to read the original
anagrams backward, upside down, or even ar
ranged in a triangle, perhaps because this act of
"restating" the problem loosens you up.
(b) Another fun word puzzle is the cipher, in which
you must decode a passage that has been en
crypted with a single-letter substitution code
(e.g., A goes to L, B goes to G, etc.) If you prac
tice these until you can do the puzzle with lit
tle or no writing down, you will stimulate your
association ability and enhance your deductive
powers and concentration.
(c) Standard crossword puzzles are OK, but not
highly recommended, as they focus on fairly
simple associations but with rather esoteric
facts. The same goes for sudoku puzzles, be
cause they involve fairly standard logic. Never
thess, they are good for building concentration
and logic skills, especially if you focus on try
ing to find new solution strategies. But don't
get addicted to these puzzles; there are so many
other things to think about!
(d) Learn to play a strategic game, such as chess
or Go. If you play cards, start concentrating on
memorizing the hands as they are played.
(e) Take up a musical instrument, or if you used to
play, start practicing again.
(f) Learn a "meditative" physical ac tivity, such as
yoga, tai chi, aikido, etc. Western sports like
golf and bowling are OK, too.
(g) Read famous fictional and true accounts of
problem solving and mental toughness. Some
of our favorites are The Gold Bug, by Edgar
Allan Poe (a tale of code-breaking); any Sher
lock Holmes adventure, by Arthur Conan Doyle
(masterful stories about deduction and concen
tration); Zen in the Art of Archery, by Eugen
Herrigel (a We stemer goes to Japan to learn
archery, and he really learns how to concen
trate); Endurance, by Alfred Lansing (a true
2.1 PSYCHOLOGICAL STRATEGIES 23story of Antarctic shipwreck and the mental
toughness needed to survive).
2.1.12 If you have trouble concentrating for long peri
ods of time, try the following exercise: teach yourself
some mental arithmetic. First, work out the squares
from 12 to 32^2. Memorize this list. Then use the iden
tity x^2 - i = (x -y) (x + y) to compute squares quickly
in your head. For example, to compute 872 , we reason
as fo llows:
872 - 3^2 = (87 - 3)(87 + 3)
= 84 ·90
= 10(80·9+4·9)
= 7560.
Hence 872 = 7560 + 3^2 = 7569. Practice this method
until you can reliably square any two-digit number
quickly and accurately, in your head. Then try your
hand at three-digit numbers. For example,
5772 = 600 .554 +23^2 = 332400 +529 = 332929.
This should really impress your friends! This may
seem like a silly exercise, but it will force you to fo
cus, and the effort of relying on your mind's power of
visualization or auditory memory may stimulate your
receptiveness when you work on more serious prob
lems.
2.1.13 It doesn't matter when you work on problems,
as long as you spend a lot of time on them, but do be
come aware of your routines. You may learn that, for
example, you do your best thinking in the shower in
the morning, or perhaps your best time is after mid
night while listening to loud music, etc. Find a routine
that works and then stick to it. (You may discover that
walking or running is conducive to thought. Try this if
you haven't before.)
2.1.14 Now that you have established a routine, oc
casionally shatter it. For example, if you tend to do
your thinking in the morning in a quiet place, try to re
ally concentrate on a problem at a concert at night, etc.
This is a corollary of the "break rules" rule on page 20.2.1.15 Here's a fun loosening-up exercise: pick a
common object, for example, a brick, and list as
quickly as possible as many uses for this object as you
can. Try to be uninhibited and silly.
2.1.16 A nice source of amusing recreational prob
lems are "lateral thinking" puzzlers. See, for example,