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?"
The state of being beset or actuated by the devil or an evil
Compulsive preoccupation with a fixed idea or unwanted feeling
or emotion, often with symptoms of anxiety
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
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?
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?
(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.
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