Conference rusure::math

588.0. "Jaywalking Paperboy" by TSE::FONSECA (Caught peeking under the rug of life...) Thu Sep 25 1986 16:37

This is a problem I used to think about as a teen-ager while
delivering my papers, although I had a guess as to the answer,
I don't know if it was right. (Later the grade for my probability & statistics
class in college pointed me towards discrete mathematics.:-)

Anyway while delivering my papers, I would have to cross a street.
Taking the most direct route would mean that I should cross at a
diagonal, taking a whole block to cross. (Talk about jaywalking!)
The problem was that the street was really a highway which had traffic
on it which would not slow down for dopes in the road.

The topography was such that the walker would have only enough time
to walk straight from the center of the road to the side of the road
to avoid traffic.  (of course this would also be enough time to walk to the
unoccupied lane from the edge.)

Although I haven't given any dimensions to the the distances in this problem,
I am not sure that they are really make much difference.

What path should the paper boy take to keep the distance walked to a
minimum? (given that a vehicle may come at any time.)
What stategies should the paper boy use if a vehicle comes down the street?

As I understand the statement of the problem, the point where the newsboy 
crosses the street is irrelevant: his total distance walked is the length 
of the block plus the width of the street. WHERE he crosses the street does 
not affect this.

If that is not the expected solution, can you restate the problem more 
clearly?

Sorry for the delayed reply.  I had anticipated that the paperboy
would walk diagonally accross or even some more complicated path
such as an S curve.

After I typed the problem set in, the answer seems a bit more
obvious, maybe I should have written the problem down way back
when, would have saved myself a foot a day! :-)

I think that (.1) suggests 90 degree turns only.

E.g.:		V
		|
		|-------------->|
			       	|
		       		|
			       	|
				V

But isn't it okay in (.0) to cross half the street, then try an ambitious
diagonal, and shift to a less ambitious diagonal if a car comes?

E.g.:		>--------\
			  \
			   \--->|
			       	|
			       	|
		       		|
				V

And shouldn't the strategy be different for different expected volumes of
traffic?

John