[net.math] The parking lot problem

gjk@talcott.UUCP (06/14/85)

This  problem  was given to me by a friend (I know the answer  to 
it):

There  is a one-way street with N parking spaces in a row on  one 
side.   N cars come along, one at a time.  Each driver has chosen 
his favorite parking spot at random from the N spaces.  He drives 
along until he reaches it and parks there if it is not taken.  If 
it  is  taken,  he continues down the road until he gets  to  the 
first  free  one he sees and parks there.   If there are no  free 
spots after his favorite one, he drives home and watches TV.

Now  the question:   What is the probability that all  N  drivers 
will  park in this parking lot?   For example,  if there are  two 
cars,  then  both  cars will park unless they've both chosen  the 
second spot, so the probability of success is 3/4.

And another,  slightly harder question:   Supposing that, instead 
of N cars,  there are K, where K<N.  What is the probability that 
all will park?
-- 
			Greg Kuperberg
		     harvard!talcott!gjk

"The eerily accurate drawing of Goetz showed the face of the 'before'
figure in comic-book ads for body-building devices."-Time Magazine, April 8