These questions were used to set the stage for an introductory discussion of information theory and of entropy.  They illustrate something of how we know what we know, something of how information lets us select from a number of alternatives, something of randomness and deviation from pure randomness... 

Nevertheless,  most of these started out as just puzzles for the fun of doing puzzles.  Many are from Martin Gardner's Scientific American feature "Mathematical Games" (MG).  Some are from the works of Jean Piaget (JP).  A couple came from psychologist Percy C Wason (PW), and one is one of the "moral dilemmas" of Lawrence Kohlberg (LK).  The rest are Knowledge for Use originals.

Click on "C" for comments on a puzzle.  (Please use "Back" to return to this page.)  These puzzles and comments predate by many years (decades!) the equivalent puzzles elsewhere on this Web site.  We also have an "answers and explanations" handout sheet which we will  prepare for Web presentation. (Its inchoate form appears as "Further Discussion" at the bottom of this page.)

"inchoate"?...Please look that one up in your Funk and Wagnalls!
TWENTY QUESTIONS
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 well-ordered and un-random as a one can get.  The pattern on the upper right is about as random and un-ordered as one can get.
 

The big, lower, pattern is almost as ordered as the well-ordered, 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 one-inch 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?
  1. 2 + 2 = 4
  2. 4 / 1/2 = 2
  3. 3 1/5 X 3 1/8 = 10
  4. 8 - (-4) = 12
  5. -10(6-6) = -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 pay-off 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 checker-patterned.  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
Further discussion