





































"Eurekas"
are sometimes insights which might find use anywhere. They are like
perceptions, "perceptions of the abstract." These Web pages explore
these "perceptions at the edges of human comprehension." Puzzles
that seem "tricky" and have points that seem to evade your notice often
give clues to the nature of that elusive edge of comprehension. 



Some puzzles seem impenetrable
at first, then suddenly:
You see it!
Eureka!
You don't see it gradually; you
don't see it in little steps; you just look at it in some
different way, and there it is.














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 pieces after each cut? 





SEE P4 STEREOGRAM 











UP 




What is the direction,
up or down, of the acceleration of a freely bouncing ball at the
bottommost point of its bounce, that is, at the instant its velocity changes
from down to up?

















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. 











SEE P4 STEREOGRAM 









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 or the shape
I'm thinking about (or both) then it is accepted. Otherwise
it is rejected. I accept the red triangle." The problem
is: May any of the remaining figures be consistently rejected?













NO 








In a set of cards each card
has a 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 vowel on one side then
it has an odd number on the other side. The problem is
to determine which cards must be turned over to test the hypothesis.
No card is to be turned over unless necessary to test the hypothesis.













I & 6 








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.



.
You are on a quiz show and the quizmaster shows you three doors.
Behind one door is the winning lottery ticket, worth tens of millions.
Behind the other two doors are copies of the 95page "instruction" booklet
that came with the first version of Windows 95. You are to pick a
door, and you get the prize which is there. You choose a door, but
now the quizmaster opens, not the door you chose, but rather one of the
other doors. There is a Windows 95 booklet. Now, the quizmaster
gives you the option of sticking with the door you chose, or picking the
other door, both of which are still closed. Should you switch or
stick?









3: 1st, 3rd, & 4th 



.........
SWITCH 








You
paddle your kayak up the river from your camp to fetch your camera which
you left on a rock upstream a bit. The river flows at a uniform 2
mi/hr. You paddle (on still water) at a uniform 3 mi/hr. It
takes 30 minutes to reach your camera. If you paddle all the way
back to your camp, how long will the return trip take?













6 MIN 








"I could care less."
 "I couldn't care less."
"The record low is minus
90°F"  "The record low is minus 90°F below zero."
What
do these statements say?  Why do some people use the wrong one?














These
are unusual puzzles. They are extremely simple. Most of them,
however, have answers that evade detection. The puzzles are simple
but difficult. They require "perceptions" of things at (or perhaps
a little outside) the edges of human comprehension. The buzzsaw
and checkerboard answers are inside the edge for most everyone. So
these might be used as exemplar for the more difficult of "perceptions",
the perception of the abstract. When you see, you know with
buzzsaw
certainty.
If you can see it, you find
it hard to believe that others don't.
If you don't see it, you
find it hard to believe that anything is there is there to see.





















Click HERE for
a set of puzzles used to help teach the concepts of information content
and entropy.
