two puzzlers - (troubleshooting training:-)

[Carl Root]

Ron Nossaman wrote:
 > I'm having a late lunch, what's your excuse? %-)

World Cup Soccer.  Got in an early AM tuning  and a mid afternoon
between games.


I'm impressed with your puzzling skills, although you really could have
given others a day to figure them out.  You maust have already known
them:-)

The apples question comes from Raymond Smullian, a Harvard math
professor would loves logic puzzles.  He's written several books
including one entitled "This Book Has No Title".  The question is
similar to the 'F's puzzle in that it is an example of the tendency to
jump to conclusions without carefully looking at all the pertinent
information.  The knee jerk answer is, of course, 'one' which is, of
course, wrong.

The connect-the-dots puzzle was taught to me by my architect grandfather
when I was but a lad.  It, too, points out the narrow constraints we put
on ourselves when trying to solve a problem.  Sometimes, you've got to
give yourself permission to go outside the lines.

Carl