How to Find a Point on a Line within a Fixed Distance
It is well known that on a line, a target point in unknown position can be found by walking a path at most 9 times as long as the distance from the start to the target point, in the worst case. This competitive factor of 9 is optimal. We investigate the case where the target is knonw to be within a fixed distance r, of the start point, and determine the optimum competitive factor, C(r) < 9, that can be achieved be a competitive strategy S(r), unter this additional assumption.
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