olving methods, rapid-style methods, and pure brute-force algorithms. Human-style solvers will typically operate by maintaining a mark-up matrix, and search for contingencies, matched cells, and other elements that a human solver can use to determine and exclude cell values.Many rapid-style solvers employ backtracking searches, with various pruning techniques in order to help reduce the size of the search tree. The term rapid-style may be misleading: Most human-style solvers run considerably faster than a rapid-style solver, although the latter takes less time to write and is more easily adapted to larger grids.  A purely brute-force algorithm is very simple and finds a solution to a puzzle essentially by "counting" upward until a string of eighty-one digits is constructed which satisfies the row, column, and box constraints of the puzzle. Rapid solvers are preferred for trial-and-error puzzle-creation algorithms, which allow for testing large numbers of partial problems for validity