Ruler Wrapping

In 1985 Hopcroft, Joseph and Whitesides showed it is NP-complete to decide whether a carpenter’s ruler with segments of given positive lengths can be folded into an interval of at most a given length, such that the folded hinges alternate between 180 degrees clockwise and 180 degrees counter-clockwise. At the open-problem session of 33rd Canadian Conference on Computational Geometry (CCCG ’21), O’Rourke proposed a natural variation of this problem called ruler wrapping, in which all folded hinges must be folded the same way. In this paper we show O’Rourke’s variation has a linear-time solution.