  This paper poses a question about a simple localization problem. The question
is if an {\em oblivious} walker on a line-segment can localize the middle point
of the line-segment in {\em finite} steps observing the direction (i.e., Left
or Right) and the distance to the nearest end point. This problem is arisen
from {\em self-stabilizing} location problems by {\em autonomous mobile robots}
with {\em limited visibility}, that is a widely interested abstract model in
distributed computing. Contrary to appearances, it is far from trivial if this
simple problem is solvable or not, and unsettled yet. This paper is concerned
with three variants of the problem with a minimal relaxation, and presents
self-stabilizing algorithms for them. We also show an easy impossibility
theorem for bilaterally symmetric algorithms.
