The Jargon File (version 4.4.7, 29 Dec 2003):

fencepost error
 n.

    1. [common] A problem with the discrete equivalent of a boundary condition,
    often exhibited in programs by iterative loops. From the following problem:
    ?If you build a fence 100 feet long with posts 10 feet apart, how many
    posts do you need?? (Either 9 or 11 is a better answer than the obvious
    10.) For example, suppose you have a long list or array of items, and want
    to process items m through n; how many items are there? The obvious answer
    is n - m, but that is off by one; the right answer is n - m + 1. A program
    that used the ?obvious? formula would have a fencepost error in it. See
    also zeroth and off-by-one error, and note that not all off-by-one
    errors are fencepost errors. The game of Musical Chairs involves a
    catastrophic off-by-one error where N people try to sit in N - 1 chairs,
    but it's not a fencepost error. Fencepost errors come from counting things
    rather than the spaces between them, or vice versa, or by neglecting to
    consider whether one should count one or both ends of a row.

    2. [rare] An error induced by unexpected regularities in input values,
    which can (for instance) completely thwart a theoretically efficient binary
    tree or hash table implementation. (The error here involves the difference
    between expected and worst case behaviors of an algorithm.)


The Free On-line Dictionary of Computing (30 December 2018):

fencepost error
lamp-post error

   1. (Rarely "lamp-post error") A problem with the discrete
   equivalent of a boundary condition, often exhibited in
   programs by iterative loops.  From the following problem: "If
   you build a fence 100 feet long with posts 10 feet apart, how
   many posts do you need?"  (Either 9 or 11 is a better answer
   than the obvious 10).

   For example, suppose you have a long list or array of items,
   and want to process items m through n; how many items are
   there?  The obvious answer is n - m, but that is off by one;
   the right answer is n - m + 1.  The "obvious" formula exhibits
   a fencepost error.

   See also zeroth and note that not all off-by-one errors
   are fencepost errors.  The game of Musical Chairs involves a
   catastrophic off-by-one error where N people try to sit in N -
   1 chairs, but it's not a fencepost error.  Fencepost errors
   come from counting things rather than the spaces between them,
   or vice versa, or by neglecting to consider whether one should
   count one or both ends of a row.

   2. (Rare) An error induced by unexpected regularities in input
   values, which can (for instance) completely thwart a
   theoretically efficient binary tree or hash coding
   implementation.  The error here involves the difference
   between expected and worst case behaviours of an algorithm.

   [Jargon File]

   (1994-12-01)