1 (MG)
What is the next letter? C
W T F S S M . . .
J F M A M J J . . .
O T T F F S S E . . .
A E F H I K L . . .


2 (MG)
Rearrange the letters of NEW DOOR to
make one word. C 

3 (MG)
Arrange six glasses as shown. The first three glasses are filled
with water, the last three are empty. By moving one glass only, change
the arrangement so that the glasses alternate empty with full. C 

4 (MG)
Two girls were born on the same day of the same month in the same year
of the same parents, yet they were not twins. Explain. C 

5(MG)
"How much will one cost?"
"Twenty cents," replied the clerk in the hardware store.
"And how much will twelve cost?"
"Forty cents."
"Okay, I'll take nine hundred and twleve."
"That will be sixty cents."
What was the customer buying? C 

6
The pattern on the upper left is about as wellordered and unrandom as
a one can get. The pattern on the upper right is about as random
and unordered as one can get.
The big, lower, pattern is almost as ordered as the wellordered, upper
left pattern. But human perception is very poor at seeing that order
because of a trick used in making this pattern. There is another
trick, however, that makes the order completely obvious. It's not
something you would be likely to think of, but once you learn how to do
it, it is quite simple and easy—and elegant. Find it. C 
o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o o o o o o o o o
o 


7 (MG)
A carpenter, working with a buzz saw, wishes to cut a wooden cube, three
inches on a side, into 27 oneinch cubes. He can do this job easily
by making six cuts through the cube, keeping the pieces together in the
cube shape. Can he reduce the number of necessary cuts by rearranging
the pices after each cut? C 

8(MG)
A wheel has ten spokes. How many spaces does it have between spokes?
C 

9 (MG)
Start with a chess board and 32 dominoes. Each domino is of such
size that exactly covers two adjacent squares on the board. The 32
dominoes therefore can cover all 64 of the chess board squares. But
now suppose we cut off two squares at diagonally opposite corners of the
board and discard one of the dominoes. Is it possible to place the
31 dominoes on the board so that all the remaining 62 squares are covered?
If not prove it impossible C 

10(MG)
Among the assertions made in this problem there are three errors.
What are they?

2 + 2 = 4

4 / 1/2 = 2

3 1/5 X 3 1/8 = 10

8  (4) = 12

10(66) = 10 C


11
(JP)
A child and an adult are sitting on opposite sides of a table. Each
has a stick with a disc attached on one end. The sticks are identical.
They lift a ball of clay off the table with the sticks by pressing on opposite
sides of the clay. Then they push their sticks into the clay.
Whose stick is likely to penetrate the clay the furthest (or do they go
in the same amount) and why? C 

12
A freeway sign reads SALEM
25 miles/40km. Another freeway sign in a few miles
reads LYNN :O::
miles/33km. The number of miles to Lynn is covered
with a splotch of mud. What number is under that splotch? C 

13
(LK)
In Europe, a woman was near death from a very bad disease, a special kind
of cancer. There was one drug that the doctors thought might save
her. It was a form of radium that a druggist in the same town had
recently discovered. The drug was expensive to make, but the druggist
was charging ten times what the drug cost him to make. He paid $200
for the radium and charged $2000 for a small dose of the drug. The
sick woman's husband Heinz went to everyone he knew to borrow the money,
but he could only get together about $1000 which was half of what it cost.
He told the druggist that his wife was dying, and asked him to sell it
cheaper or let him pay later. But the druggist said, "No, I discovered
the drug and I'm going to make money from it." Heinz got desparate
and broke into the man's sotre to steal the drug for his wife. Should
the husband have done that? Was it right or wrong? C 

14
Two players play a game in which each person chooses one of two "plays,"
A or B, without the other knowing what his choice is. The choices
are recorded, and then each player is paid according to this payoff matrix
—>
The first number is X's winnings; the second is Y's. One hundred
games are played in succession. What strategy should a player use?
(The players do not communicate with each other.) C 
Y's choice
X's
choice

A

B

A

(+9, +9)

(10, +10)

B

(+10, 10)

(9, 9)


15
(JP)
Is there a relationship between happy face and curly hair in either of
these sets of faces? Is one set showing a clearer correlations between
happy face and curls? C 

16
(PW)
Start with four figures: a red square, a blue triangle, a red triangle,
and a blue square. Someone says, "I am thinking about one of the
colors and one of the shapes, and if a figure has either the color of the
shape I'm thinking about (or both) then it is accepted. Otherwise
it is rejected. I accept the white triangle." The problem
is: May any of the remaining figures be consistently rejected? C 

17(PW)
In a set of cards each card has number on one side and a letter on the
other. Four cards are lying on a table. They show an "I," an
"N," a "6," and a "3". Someone suggests the hypothesis:
If a card has a consonant on one side then it has an even number on the
other side. The problem is to detemine which cards must be turned
over to test the hypothesis. No card is to be turned over unless
necessary to test the hypothesis. C 

18
Devise a scheme for arranging ellipses such that any two ellipses that
are similar to each other are near each other; any two that are near each
other are similar to each other; and any ellipse will fit into the scheme.
C
This new (Jan, 2000) graphic
was made so you might download it, print it, cut out the ellipses, and
then try out various arrangements.
> 

19
Two of the nine numbered patterns are completely random. Which two?
What are the ordering schemes for each of the remaining seven patterns?
Some are merely repeated simple patterns; others are a bit more subtle,
but none requires sophisticated techniques to discover. C 

20 (MG)
Five cards are placed in a row as shown. All card backs are either
marble or checkerpatterned. Are all the cards with marble backs
aces? The problem is not to answer the question but to determine
the minimum number of cards that must be turned over in order to answer
it. C 
