fencepost error

fencepost error n.  1. 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.)