1  Five-year-olds usually get the fourth part of this one more easily than adults.  That odd fact demonstrates the distinction between “iconic” information and “symbolic” information (Jerome Bruner).
 
 
 
 
 
 
 
 
 
 
 

2   3   4   10   Examples of misleading clues and the need to break out of conventional thinking.  (These are from Martin Gardner's “April Fool” puzzle set.)
 
 
 
 
 
 
 
 
 
 
 
 

5  Illustrates where the “ln” in S = k ln W comes from.
 
 
 
 
 
 
 
 
 
 
 
 

6  Illustrates: a) Random vs well ordered patterns; and b) Stereopsis and extension of ordinary perception.  This leads to the concept of autocorrelation.  Several routes from here can be taken toward the notion of predictability at the level of particle interactions, which is a basic concept underlying entropy.
 
 
 
 
 
 
 
 
 
 
 

7   9   Illustrates the “Eureka!” phenomenon and the experience of knowing when you have the right answer—and also knowing that an answer accompanied by extensive, intricate hard-to-understand explanation might be known to be wrong without needing to work out the dreary details.
 
 
 
 
 
 
 
 
 
 
 
 

8   One specific sense of symmetry can make the answer obvious.  This one particularly well illustrates that what is “obvious” to one person can be quite obscure to another person.  (Another “April fool” puzzle.)
 
 
 
 
 
 
 
 
 
 
 

11   A question used by Piaget to test for development (not learning) of a sense of mutually reciprocal  relationships and a specific kind of sense for symmetry.
 
 
 
 
 
 
 
 
 
 
 

12   Tests for a sense of ratio and proportion.  One item of evidence for the widespread weakness of this sense is seen in the widespread failure to sense meaning of very large numbers, the kind of numbers common in national monetary figures.  Taxes of $100 billion and of $100 million are often not seen as being particularly different, just staggeringly large.  Portion out a tax among the population who must pay it, and the difference becomes clear, quite “obvious.”  One tax is about $400 per person; the other, 40 cents.
 
 
 
 
 
 
 
 
 
 
 
 

13   There is no “The Answer” for this one.  It is one of several moral dilemmas—the most well known of them—used by Harvard’s Lawrence Kohlberg for studying development of moral judgements.  Kohlberg’s studies incorporate both learning and developmental elements.  Different people give different reasons for their answers to these problems, and those differences can be associated with different developmental sophistications.
   Questions about moral relativism can sometimes be resolved by incorporating multielement elements into the argument:  A moral judgement that incorporates a given element of logical insight is superior to another judgement that does not, but only in that single criterion of ranking.  One of Kohlberg’s concerns is the symmetry logic seen in 11 above.
 
 
 
 
 
 
 
 
 
 
 

14   A simple zero-sum game from classical game theory.  It illustrates an advantage of cooperation (logical equivalence relationship) over competition (mutual exclusion). When E = mc² is seen as indicating the conversion of mass to energy, an equivalence is being incorrectly seen as a mutual exclusion.
 
 
 
 
 
 
 
 
 
 
 
 

15   A peek into the roots of statistical reasoning.  A probe to see if all possibilities are recognized as important in a simple two-element logic problem.  Statistics is usually recognized as treating uncertainties; statistics also treats multiple elements and attempts to sort them out and properly relate them.  The most common error when trying tosolve this puzzle is to ignore the disconfirming evidence.
 
 
 
 
 
 
 
 
 
 
 

16   Demonstrates the simple but difficult logical relationship of  either/or (or both), one of the 16 binary logical relationships.  These 16 are quite often confused one with another.
 
 
 
 
 
 
 
 
 
 
 
 
 

17   Today, perhaps the quintessential “simple but difficult” puzzle.  (However, Marilyn vos Savant’s door selection puzzle, as published and debated in Parade magazine is now even more widely known and is probably destined to become an even better example, considering the sharp some-see-it/some-don’t dichotomy it evokes.)  Wason’s card selection puzzle demonstrates the difficult most people have in recognizing the relationship of logical (Boolean) implication.  "Capacity to do work implies energy" is true.  The inverse, "energy implies capacity to do work," is not true.  Capacity to do work cannot be the same thing as energy because other influences, especially entropy, can render energy unavailable for doing work.  Energy is necessary for capacity to do work, but not sufficient.  This distinctions is apparently not “seen” by those occasional physics textbooks authors who define energy as capacity to do work.
 
 
 
 
 
 
 
 
 
 
 
 
 

18   A two-component measure.  Visually illustrates the impossibility of unique rank order by a measure more complex than single-component measure (scalar).  (Color is a three-component measure; ordering colors is another demonstration of this principle.)  A core element in the concept of degrees of freedom.
 
 
 
 
 
 
 
 
 
 
 
 
 
 

19   Order within chaos.  An element in the concept of information content, and in entropy.  Illustrates why “order” lowers the number of symbols needed to describe.  The patterns illustrate that potential elements of perception might be absent: when dot patterns interpenetrate, the perception of  order we do have is overwhelmed. The large pattern in question #6 illustrates both the overwhelming and an extension of perception that overcomes the difficulty.  This puzzle is also found on this site at "randomdot.html"; answers are linked from that page, and the "secret" to that link is revealed in a link from the PlatinumPlover Egg.
 
 
 
 
 
 
 
 
 
 
 
 
 

20   Martin Gardner’s diabolical twist on 17) above.  The problem must be read very carefully, and extraneous assumptions that are not really stated in the problem must be eliminated.