by Paul Niquette
Copyright ©1996 Resource Books All rights reserved.

obsession n. 

  1. The state of being beset or actuated by the devil or an evil spirit. 
  2. Compulsive preoccupation with a fixed idea or unwanted feeling or emotion, often with symptoms of anxiety
"A bottle and a cork cost a dollar ten cents," said my father in the late 1930s.  "The bottle costs a dollar more than the cork.  How much does the cork cost?"
That is the first "word problem" I can remember.  And I am still using it more than a half-century later with grandchildren and with fellow techies, occasionally as a qualifier during interviews.
Another one my father gave me makes a vital point about "reciprocal arithmetic"...
An automobile averages 30 miles per hour during the first half of a trip.  How fast does it have to travel during the second half to average 60 miles per hour for the whole trip?
Solving problems has held a life-long primacy as my most practical passion.  There is too much volition involved for me to use the word "obsession."  If it is an obsession, it is magnificent.

In school, I tackled all the exercises at the end of each chapter, even when only the even ones were assigned -- often instead of studying the chapter.

One problem, a closed form analysis of vehicular flow, provided a few hours per month of pure intellectual pleasure for nearly a quarter of a century.  I have its solution filed away in a notebook, entitled, appropriately, "Density Lock."

Who else owns a shelf of books full of problems?  I like to take a volume out of my briefcase immediately after the oxygen-mask demonstration.  Not the best way to meet chicks, perhaps, but, while my head is screwed into a problem, the slowest airliner achieves Mach 3.

And who else likes to create problems?  Problems, not troubles!  Try these.

A certain bicyclist commutes on a level road.  One day he/she discovers a shortcut over a hill.  The person-of-the-wheel estimates that his/her speed pedalling up the hill will be half that of coasting down the hill.  Should he/she take the shortcut?

Take the least significant digit of a number and move it to the leftmost position, shifting the rest of the digits to the right one position.  The resulting number is nine times the initial number.  What is the smallest such number?

Consider two boxes, each capable of concealing three balls.  One box contains two white balls and one black, the other two black balls and one white.  You are permitted to remove one ball from either box without seeing inside.  I will wager even money that you cannot match the color of a second ball removed from either box with the first ball.  Will you accept the wager?

Suppose there to be a band tight around the earth.  If the band were lengthened by 10 feet and the resulting gap distributed uniformly, would there be room...

  (a) for a tall person to walk under?
  (b) for a thin person to crawl under?
  (c) for a razor blade to slide under?
  (d) for a virus to swim under?
  (e) none of the above.
A mathematician owns a tortoise and a hare, the latter being capable of a speed much faster than the former.  One day they set out together toward point P a unit distance from origin O.  The hare arrives at P and returns to meet the tortoise, then dashes forward again to point P.  The hare returns to the tortoise, to point P, and so forth, ad infinitum. The next day, they set out together, but this time the hare returns from point P to the origin O on each cycle, dashing back and forth between O and P until the tortoise arrives at P.  On which day does the hare travel the greatest distance?

The full moon can be eclipsed by a penny held no further from the naked eye than...

   (a) 3' 10-5/8"
   (b) 4' 10-5/8"
   (c) 5' 10-5/8"
   (d) 6' 10-5/8"
   (e) all of the above

Imagine writing programs which automatically generate problems. Problems not solutions.  What is the next entry in each?

  0, 2,  8, 30, 128, ___
  0, 2, 10, 42, 188, ___
  0, 3, 16, 69, 312, ___
  0, 4, 20, 84, 376, ___

And so forth.  Enough to fill volumes (see Problems with a Purpose).  I blame my father, of course.  With deepest gratitude.

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