The torch problem (also known as the bridge problem or the flashlight problem) is about getting a number of people across a bridge as quickly as possible under certain constraints. Although a very simply stated problem, the solution is surprisingly non-trivial. The case in which there are just four people and the capacity of the bridge is two is a well-known puzzle, widely publicised on the internet. We consider the general problem where the number of people, their individual crossing times and the capacity of the bridge are all input parameters. We present an algorithm that determines the shortest total crossing time; the number of primitive computations executed by the algorithm (i.e. the worst-case time complexity of the algorithm) is proportional to the square of the number of people.


algorithm derivation shortest path dynamic programming algorithmic problem solving 


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  1. 1.
    Backhouse, R.: Algorithmic problem solving. Lecture notes, School of Computer Science, University of Nottingham. Updated at least annually and widely available on the internet, but see author’s website for latest versionGoogle Scholar
  2. 2.
    Backhouse, R.: Regular algebra applied to language problems. Journal of Logic and Algebraic Programming (66), 71–111 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Rote, G.: Crossing the bridge at night. Bulletin of the European Association for Theoretical Computer Science 78, 241–246 (2002)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roland Backhouse
    • 1
  1. 1.School of Computer Science University of NottinghamNottinghamEngland

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